Re: a macro

[Meikel Brandmeyer]

Hi,

On 13 Okt., 08:56, Laurent PETIT  wrote:

> So in short: calling eval from the macro, on its argument.

Beware the leopard!

user=> (defn f
 [constant]
 `(+ x# (* ~constant y#)))
#'user/f
user=> (defn variables*
 [form]
 (if (seq? form)
   (reduce into [] (map variables* form))
   (when (and (symbol? form) (nil? (resolve form)))
 [form])))
#'user/variables*
user=> (defmacro variables
 [form]
 `(variables* (quote ~form)))
#'user/variables
user=> (defmacro dynamic?-variables
 [form]
 `(variables ~(eval form)))
#user/dynamic?-variables
user=> (dynamic?-variables '(+ x (* 2 y)))
[x y]
user=> (dynamic?-variables (+ x (* 2 y)))
java.lang.Exception: Unable to resolve symbol: x in this context
(NO_SOURCE_FILE:18)
user=> (dynamic?-variables (f 2))
[x__12__auto__ y__13__auto__]
user=> (let [x 2] (dynamic?-variables (f x)))
java.lang.InstantiationException: user$eval48$eval49__50
(NO_SOURCE_FILE:52)

One has to be aware of the limitations of such an approach.

Sincerely
Meikel

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Re: a macro

[Sunil S Nandihalli]

basically the following is the macro that creates a function from the
expression calculated using mathematica.. it seems to be doing something
still not the whole thing.. hopefully some of you may be able to help me.


(defmacro sexp2fn [sexp]
  (let [sym (eval sexp)
vars (eval (math (Variables sexp)))]
(println [sym vars])
`(fn ~vars
~sym)))

;; when I macro expand the following

(sexp2fn (mathematica-eval "D[x*x+x*y,x]"))

;; I get the error whose stack trace is

Unable to resolve symbol: sexp in this context
  [Thrown class java.lang.Exception]

Restarts:
 0: [QUIT] Quit to the SLIME top level

Backtrace:
  0: clojure.lang.Compiler.resolveIn(Compiler.java:5677)


;; however if I replace the above macro with the following

(defmacro sexp2fn [sexp]
  (let [sym (eval sexp)
vars []]   ;(eval (math (Variables sexp)))]
(println [sym vars])
`(fn ~vars
~sym)))

;and I macro expand the same expression i get
(clojure.core/fn [] (+ (* 2 x) y))

; as you can see the arguments list is empty .. i would have liked to have
[x y] over there and (math (Variables (+ (* 2 x) )y) would return [x y] but
for some reason sexp is not visible .. can anybody help?

does eval have any lexical scope in which it will run or does it run in the
null-lexical scope?
Sunil.

On Wed, Oct 13, 2010 at 2:27 PM, Meikel Brandmeyer  wrote:

> Hi,
>
> On 13 Okt., 08:56, Laurent PETIT  wrote:
>
> > So in short: calling eval from the macro, on its argument.
>
> Beware the leopard!
>
> user=> (defn f
> [constant]
> `(+ x# (* ~constant y#)))
> #'user/f
> user=> (defn variables*
> [form]
> (if (seq? form)
>   (reduce into [] (map variables* form))
>   (when (and (symbol? form) (nil? (resolve form)))
> [form])))
> #'user/variables*
> user=> (defmacro variables
> [form]
> `(variables* (quote ~form)))
> #'user/variables
> user=> (defmacro dynamic?-variables
> [form]
> `(variables ~(eval form)))
> #user/dynamic?-variables
> user=> (dynamic?-variables '(+ x (* 2 y)))
> [x y]
> user=> (dynamic?-variables (+ x (* 2 y)))
> java.lang.Exception: Unable to resolve symbol: x in this context
> (NO_SOURCE_FILE:18)
> user=> (dynamic?-variables (f 2))
> [x__12__auto__ y__13__auto__]
> user=> (let [x 2] (dynamic?-variables (f x)))
> java.lang.InstantiationException: user$eval48$eval49__50
> (NO_SOURCE_FILE:52)
>
> One has to be aware of the limitations of such an approach.
>
> Sincerely
> Meikel
>
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Re: a macro

[Meikel Brandmeyer]

Hi,

On 13 Okt., 11:19, Sunil S Nandihalli 
wrote:

> (defmacro sexp2fn [sexp]
>   (let [sym (eval sexp)
>         vars (eval (math (Variables sexp)))]
>     (println [sym vars])
>     `(fn ~vars
>         ~sym)))

Try the following:

(defn evaled-variables
  [form]
  (eval `(math (Variables ~form

(defmacro sexp2fn
  [string]
  (let [form (mathematica-eval string)
vars (evaled-variables form)]
   `(fn ~vars ~form)))

Using my previous stubs I get:

user=> (macroexpand-1 '(sexp2fn 2))
(clojure.core/fn [x__1__auto__ y__2__auto__] (clojure.core/+
x__1__auto__ (clojure.core/* 2 y__2__auto__)))

You would call it (sexp2fn "D[x*x+x*y,x]").

Hope that helps.

Sincerely
Meikel

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Re: Problems with clojure couchdb

[Moritz Ulrich]

On Wed, Oct 13, 2010 at 4:00 AM, Mark Engelberg
 wrote:
> On Tue, Oct 12, 2010 at 6:41 AM, Moritz Ulrich
>  wrote:
>> Regarding your error: Maybe you open too many sockets which don't get
>> closed and your process runs out of file descriptors.
>
> Yes, I think that's the problem.  I found a blurb on the net about how
> to expand the range of usable ports for sockets, but instead I went
> the route of writing my documents in batches of 50 as both of you
> suggested.  This didn't entirely solve the problem, but it definitely
> helped and I was able to get much further.  But after entering about
> 2,000,000 small documents, the database size was nearing 4GB and couch
> seemed to really crawl to add new documents.  I like couch's
> ease-of-use alongside Clojure, but I think I need something that isn't
> quite so space-hungry and remains fast for largish collections.  So
> I'm thinking I'm going to have to punt on couch db.  Any other tips on
> what I might be doing wrong, or does this sound typical?
>
> Thanks,
>
> Mark
>

Do you update your documents often? CouchDB keeps old versions of
documents in the database. To remove them, do a "compact" on the
database.
If you don't update your documents often, you could have a look at the
config parameters. However, I'm not sure if that will bring you the
desired results.


-- 
Moritz Ulrich
Programmer, Student, Almost normal Guy

http://www.google.com/profiles/ulrich.moritz
BB5F086F-C798-41D5-B742-494C1E9677E8

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Re: Creating a new library

[lprefontaine]

Good to know... is this written somewhere ? I looked at Clojars yesterday
but did not find anything...

Luc P.

Saul Hazledine  wrote ..
> On Oct 13, 5:31 am, lprefonta...@softaddicts.ca wrote:
> > As far a publishing to Clojars, I do not know the policy.
> > Uploading various jars maintained by other teams not involved in
> > Clojure may "pollute" the repo along the way.
> >
> 
> As I understand it, its fine to put jars from other projects on
> Clojars. If you do this, it is recommended to use your own groupid or
> org.clojars. as the groupid. That way people know that
> the jar files aren't from the originating team. If the originating
> team ever puts their package on the central maven repository the
> clojars package won't be picked up by mistake by people who want the
> official package.
> 
> Saul
> 
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Re: Help to optimize palindrome search from input file

[Stephen C. Gilardi]

On Oct 12, 2010, at 3:02 PM, tonyl wrote:

> (defn palindrome? [s]
>  (= s (reduce str (reverse s

One opportunity to micro-optimize is to replace "reduce str" with "apply str". 
str uses a StringBuilder object to build a string from its arguments. When you 
use reduce, the code walks down s appending the result so far with the next 
string, creating a new StringBuilder object each time. When you use apply, str 
creates one StringBuilder object and passes all the remaining elements of s to 
it.

The amount of improvement depends on the length of s. In a micro-benchmark I 
did just now, using apply reduced the overall runtime of the benchmark by a 
factor of 4.8. (pun acknowledged).

--Steve

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Re: Creating a new library

[Saul Hazledine]

On Oct 13, 1:21 pm, lprefonta...@softaddicts.ca wrote:
> Good to know... is this written somewhere ? I looked at Clojars yesterday
> but did not find anything...
>

Its mentioned near the end of the tutorial:
  http://github.com/ato/clojars-web/wiki/tutorial

Saul

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Re: Creating a new library

[Meikel Brandmeyer]

Hi,

On 13 Okt., 07:59, Saul Hazledine  wrote:

> As I understand it, its fine to put jars from other projects on
> Clojars. If you do this, it is recommended to use your own groupid or
> org.clojars. as the groupid. That way people know that
> the jar files aren't from the originating team. If the originating
> team ever puts their package on the central maven repository the
> clojars package won't be picked up by mistake by people who want the
> official package.

I find this to be greatly abused by the people. Sometimes you have to
scroll through several pages of search results only to find the
original project jar by accident. There is no documentation whatsoever
what is changed in the different variants. Sometimes they are even
uploaded under non-org.clojars groups giving even a little official
touch. I had one user having trouble to set up vimclojure who said
that he downloaded random vimclojure jars because he couldn't tell
which is the official one.

All-in-all I think that an easy accessible repository is a big Good
Thing(tm). But the org.clojars groups where a bad idea, IMHO. If a
dependency doesn't have artifacts on clojars, there is always the
possibility of approaching the original project team on the issue. If
you really need jars which are modified in some way (eg. a bugfix
which hasn't made it upstream, yet), they should be put into a local
repo, be it .m2 or something like archiva (BTW: Thanks for this tip,
Luc)

Sincerely
Meikel

PS: all that said, I'm guilty myself of putting stuff in
org.clojars.kotarak...

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Re: New Release of the Clojure Debugging Toolkit

[atreyu]

I suppose it could be a way to unify both versions using (System/
getProperty "path.separator") and (System/getProperty
"file.separator")
I try to fix it like Leo but i get a regexp exception using (reval)
with \

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Re: Creating a new library

[lprefontaine]

I need a new pair of eyes...

Saul Hazledine  wrote ..
> On Oct 13, 1:21 pm, lprefonta...@softaddicts.ca wrote:
> > Good to know... is this written somewhere ? I looked at Clojars yesterday
> > but did not find anything...
> >
> 
> Its mentioned near the end of the tutorial:
>   http://github.com/ato/clojars-web/wiki/tutorial
> 
> Saul
> 
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Re: New Release of the Clojure Debugging Toolkit

[atreyu]

I suppose it could be a way to unify both versions using (System/
getProperty "path.separator") and (System/getProperty
"file.separator")
I add the leo changes (to master vesion -lesses changes-) and it works
for me
thanks!!

On Oct 12, 2:53 pm, leo  wrote:
> This works for me under Windows 7. I set all forward slashes paths in
> my .emacs file like this:
>
> (progn
>   (setq cdt-dir "c:/msysgit/cdt")
>   (setq cdt-source-path "c:/clj/clojure-1.2.0/src/jvm;c:/clj/
> clojure-1.2.0/src/clj;c:/clj/clojure-contrib-1.2.0/src/main/clojure/
> clojure/contrib;")
>   (load-file (format "%s/ide/emacs/cdt.el" cdt-dir)))
>
> And these are the diffs from George's current windows version
> (hopefully George will be able to make them available in a more
> convenient way) - and note the "file:///" with 3 slashes under
> Windows:
> -
> diff --git a/.gitignore b/.gitignore
> diff --git a/README b/README
> diff --git a/docs/cdt.muse b/docs/cdt.muse
> diff --git a/docs/emacs-cdt.muse b/docs/emacs-cdt.muse
> diff --git a/ide/emacs/cdt.el b/ide/emacs/cdt.el
> index 0560ab2..42e3e1a 100644
> --- a/ide/emacs/cdt.el
> +++ b/ide/emacs/cdt.el
> @@ -25,13 +25,13 @@
>    (gud-call (format "(reval-display '%s)" (thing-at-point 'sexp
>
>  (defun strip-trail (path)
> -  (if (= (elt path (- (length path) 1)) ?\\)
> +  (if (= (elt path (- (length path) 1)) ?/)
>        (substring path 0 (- (length path) 1))
>      path))
>
>  (defun cdt-query-cmdline ()
>    (let ((path (strip-trail cdt-dir)))
> -    (format "java -classpath%s\\lib\\clojure-1.2.0.jar;%s\\lib\
> \clojure-contrib-1.2.0.jar;%s\\lib\\debug-
> repl-0.3.0-20091229.021828-3.jar;%s\\src clojure.main --repl"
> +    (format "java -classpath%s/lib/clojure-1.2.0.jar;%s/lib/clojure-
> contrib-1.2.0.jar;%s/lib/debug-repl-0.3.0-20091229.021828-3.jar;%s/src
> clojure.main --repl"
>             path path path path)))
>
>  (defun cdt (port)
> diff --git a/project.clj b/project.clj
> diff --git a/src/com/georgejahad/cdt.clj b/src/com/georgejahad/cdt.clj
> index d479877..d2d570f 100644
> --- a/src/com/georgejahad/cdt.clj
> +++ b/src/com/georgejahad/cdt.clj
> @@ -21,10 +21,11 @@
>  ;; add-classpath is ugly, but handles the fact that tools.jar and
>  ;; sa-jdi.jar are platform dependencies that I can't easily put in a
>  ;; repo:
> -(with-out-str (add-classpath (format "file://%s/../lib/tools.jar"
> +(with-out-str (add-classpath (format "file:///%s/../lib/tools.jar"
>                                       (System/getProperty
> "java.home"
> -(with-out-str (add-classpath (format "file://%s/../lib/sa-jdi.jar"
> +(with-out-str (add-classpath (format "file:///%s/../lib/sa-jdi.jar"
>                                       (System/getProperty
> "java.home"
> +
>  (import com.sun.jdi.Bootstrap
>          com.sun.jdi.request.EventRequest
>          com.sun.jdi.event.BreakpointEvent
> @@ -90,7 +91,7 @@
>  (defonce source-path (atom ""))
>
>  (defn remove-trailing-slashes [s]
> -  (str/replace s "\\;" ";"))
> +  (str/replace s "/:" ":"))
>
>  (defn set-source-path [path]
>    (reset! source-path (remove-trailing-slashes path)))
> @@ -98,10 +99,10 @@
>  (defn get-source []
>    (let [file (.sourcePath (.location (.frame (ct) (cf
>          paths (.split @source-path ";")]
> -    (if (= (first file) \\)
> +    (if (= (first file) \/)
>        file
>        (first (filter #(.exists (java.io.File. %))
> -                     (for [p paths] (str p "\\" file)))
> +                     (for [p paths] (str p "/" file)))
>
>  (defmacro check-unexpected-exception [& body]
>    `(try
> @@ -325,11 +326,11 @@
>      (re-pattern (str s "\\$"
>
>  (defn fix-class [c]
> -  (str/replace c "/" "."))
> +  (str/replace c "\\" "."))
>
>  (defn get-class* [fname]
>    (->> (.split @source-path ";")
> -       (map #(re-find (re-pattern (str % "\\(.*)(.clj|.java)"))
> fname))
> +       (map #(re-find (re-pattern (str % "/(.*)(.clj|.java)"))
> fname))
>         (remove nil?)
>         first
>         second
> @@ -426,7 +427,7 @@
>  (defn get-file-name [frame]
>    (let [sp (try (.sourcePath (.location frame))
>                  (catch Exception e "source not found"))]
> -    (last  (.split sp "\\"
> +    (last  (.split sp "/"
>
>  (defn clojure-frame? [frame fields]
>    (let [names (map #(.name %) fields)]
>
> On Oct 11, 6:48 pm, atreyu  wrote:
>
> > Hi folks and congrats to George Jahad for this great work.
> > Hoewer the cdt dont work on my windows vista. After some changes on my
> > own i get the same error of Greg Willams:
>
> > java.lang.ClassNotFoundException: com.sun.jdi.Bootstrap (cdt.clj:28)
>
> > i've tried add-classpath of tool.jar (where is the class in my jdk)
> > with various formats,
> > after testing the urls in browser with success but i get the
> > ClassNotFound all the time
>
> > Current directory is c:/Users/atreyu/AppData/Roaming/.emacs.d/
> > Clojure 1.2.0
> > user=> java.lang.ClassNotFoundException: com.sun.jdi.Bootstrap
> > (cdt.clj:28)
> > user=> java.lang.Exce

Override print-method of struct

[andrei]

How can I override print-method for a map, defined with defstruct?

I have to create object hierarchy: one map is a parent for another,
i.e. it holds link to a child, and another is a child for the first
one, i.e. holds link to a parent. When I try to print it, I get
StackOverflowError since printer tries recursively print objects:

 parent -> child -> parent -> child -> 

The best solution I see is to override print-method or str, so the
printing will go normally. I found this topic:

http://groups.google.com/group/clojure/browse_thread/thread/4a675222f208899d

which shows how to override print-method for objects defined by
deftype, but is there a way to do same trick for maps? Maybe it is
possible to add some special tag to object's meta? Or to redefine
print-method in the only namespace?

Or maybe I'm just looking at the wrong direction?

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Re: precise numbers

[Nicolas Oury]

On Tue, Oct 12, 2010 at 8:35 PM, cej38  wrote:
> The more that I think about it, the more I would rather have a set of
> equalities that always work.  float= was a good try.
>
>

The only way to do so is to have numbers with infinite precision.

For example as lazy-seq of their digits.

But:
- it is slow
- equality is semi-decidable only.

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Re: strange bug in range or lazy-seq?

[Stuart Halloway]

After thinking about it some more, I don't understand it either.  I have 
created a ticket for this: 
https://www.assembla.com/spaces/clojure/tickets/457-lazy-recursive-definition-giving-incorrect-results.

As a workaround, eliminate the lazy intermediary "nums" sequence, e.g. 

(def primes
(concat
 [2]
 (lazy-seq
  (let [primes-from
(fn primes-from
  [n]
  (if (some #(zero? (rem n %))
(take-while #(<= (* % %) n) primes))
(recur (+ n 2))
(lazy-seq (cons n (primes-from (+ n 2))]
(primes-from 3)

Stu

> Thank you all for explaining this to me but I still don't understand
> clojures behavior in this case,
> 
> Try running this code:
> 
> (def nums (drop 2 (range)))
> (def primes (cons (first nums)
>  (lazy-seq (->>
>(rest nums)
>(remove
>  (fn [x]
>(let [dividors (take-while #(<= (* % %) x)
> primes)]
>  (println (str "primes = " primes))
>  (some #(= 0 (rem x %)) dividors
> (take 5 primes)
> 
> It prints out:
> (primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> primes = (2)
> 2 3 5 7 9)
> 
> How can (println primes) ever print out (2) ? That means that primes
> must have length 1 and that should be impossible no matter how chunked
> it is. It's hard to believe that that is intended behavior.
> I don't insist that a recursive lazy definition needs to work. It
> could also throw an error. But simply giving incorrect and
> unpredictable results can't be a good solution in my opinion.
> 
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Re: precise numbers

[Felix H. Dahlke]

Nice rant, I learned something here :) I somehow thought BigDecimal
wouldn't have any precision issues, but I probably never noticed because
I can only think in base-10 arithmetic. Has been good enough for my
humble precision problems so far though, never had a notable performance
issue with it either.

On 12/10/10 23:44, Brian Hurt wrote:
> 
> 
> On Tue, Oct 12, 2010 at 3:35 PM, cej38  > wrote:
> 
> The more that I think about it, the more I would rather have a set of
> equalities that always work.  float= was a good try.
> 
> 
> 
> 
> 
> Every fucking language I've ever worked on has had this problem- "floats
> are broken!"  And every single one, people keep coming up with the same
> wrong answers to this.  C, Java, Ocaml, Haskell, SQL, now Clojure. 
> Makes me wonder what language you are coming from where floats *aren't*
> broken.  Some languages patch their print methods to hide the errors in
> the simple cases, but I've yet to see one where 0.1 + 0.1 + 0.1 + 0.1 +
> 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 = 1.0.  Try it in the language of your
> choice.
> 
> First of all, the base of the floating point number just changes what
> fractions "break".  For example, in base 10, 1/3 * 3 = 0.9...  So
> no, going to base-10 doesn't save you.  IEEE 754 floats are base-2, so
> 1/10th is impossible to represent precisely, the same way 1/3 is
> impossible to represent precisely in base-10.  Oh, and Clojure has, from
> it's Java roots, a BigDecimal class which does do base-10 arithmetic. 
> 
> And no, going to rationals doesn't save you either.  Take the vector [1,
> 0, 1], and normalize it so it's euclidean length is 1, without error. 
> Have a nice day.  *Any* finite precision representation is going to have
> round off error.  Oh, and Clojure does have a rational class.
> 
> And once you have round-off, you're going to have numeric errors.  At
> which point, how you deal with those errors is important.  Numeric
> algorithms fall into two broad categories- stable and unstable.  With
> stable algorithms, errors tend to cancel each other, so your final
> answer is going to be pretty close to correct.  With unstable
> algorithms, errors tend to accumulate (I'm simplifying here for the
> newbies, for those who know what I'm talking about).
> 
> No, throwing more bits at the problem won't save an unstable algorithm,
> it'll just take longer for the unstable algorithm to finally destroy any
> and all accuracy.  Double precision numbers give you enough precision to
> measure the distance from here to the moon- in multiples of the
> wavelength of red light.  Precisely.  Also note there is a difference
> between precision and accuracy- if I say pi is equal to
> 3.179830482027405068272948472, that's very precise- but not very
> accurate.  Unstable algorithms destroy accuracy, not precision.
> 
> And no, ranged floats don't help either- as they grossly overestimate
> the error of stable algorithms.  A classic example of a super-stable
> algorithm is Newton's method- generally, the number of bits of precision
> is doubled (or more) every iteration, as the algorithm converges to the
> answer. But ranged floats have the error increasing every iteration.
> 
> Oh, and double precision floating point numbers (especially if they're
> unboxed) are between 10x and 1000x as fast as other representations-
> thanks to hardware acceleration.  Your CPU can execute one floating
> point operation a clock cycle, two if it's vectorized code.
> 
> Floating point is not broken.
> 
> 
> 
> Brian
> 
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Seen in #clojure – October 7th w/ maybe-m monad

[Jacek Laskowski]

Hi,

I was reading the blog entry Seen in #clojure – October 7th [1] and
couldn't stop thinking it might be easier with monads. Since I'm new
to monads, Clojure and functional programming in general I'd
appreciate any comments on my solution, esp. with regards to maybe-m
monad's use. I guess there should be a way to ease weeks, days, hours
and minutes functions since they all share the same structure.

Any tips on doing it in a Clojure idiomatic way *with* monads are
greatly appreciated. Thanks.

(defn weeks
  [v]
  (let [divider (* 60 24 7)]
[(int (/ v divider))(rem v divider)]))

(defn days
  [v]
  (let [divider (* 60 24)]
[(int (/ v divider))(rem v divider)]))

(defn hours
  [v]
  (let [divider 60]
[(int (/ v divider))(rem v divider)]))

(defn minutes [v]
  (second (hours v)))

(defn expand-minutes
  [i]
  (domonad maybe-m
[[ms remaining] (weeks i)
[ds remaining] (days remaining)
[hs remaining] (hours remaining)]
(println ms "weeks" ds "days" hs "hours" remaining "minutes")))

[1] http://matthewm.net/blog/2010/10/13/seen-in-clojure-october-7th

Jacek

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Re: precise numbers

[David Sletten]

On Oct 12, 2010, at 5:44 PM, Brian Hurt wrote:

>   For example, in base 10, 1/3 * 3 = 0.9...  

It may seem counterintuitive, but that statement is perfectly true.
1 = 0....

That's a good test of how well you understand infinity.

Of course, the problem arises when we truncate the string of 9's, which we must 
invariably do in a computer-based representation.

Have all good days,
David Sletten




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Re: Test-driven development in Clojure

[Felix H. Dahlke]

I see. So instead of using interfaces and implementations of these, I
would simply use closures, one for mock and one for production? That was
actually my first attempt, but I didn't like it back then.

Take this code for example - passing a function just to have it called
feels weird:

(defn load-page [provider name]
  (provider name))

(load-page (make-mock-provider) "home")

In Java, this would probably look like this:

class PageLoader {
Provider provider;

PageLoader(Provider p) {
provider = p;
}

Page loadPage(String name) {
provider.loadPage(name);
}
}

PageLoader l = new PageLoader(new MockProvider());
l.loadPage("home");

Then again, it might just feel weird because I've gotten very used to
OOP. In my Java code, loading pages is a responsibility of the
PageLoader and it delegates it to the Provider. Objects have
responsibilities and send messages to each other to fulfill these,
that's OOP.

In functional programming, there's simply a function that has a certain
functionality, and everything it needs to fulfill it has to be provided
by the caller. That's at least how I understand it by now.

Maybe I should just call the function returned by (make-mock-provider)
directly? The interface in Java has the great benefit of ensuring type
safety (plus there's no closures yet, so it's the only way), but does
this make sense in a dynamic language? I mean, if I passed an
implementation of the wrong interface or a closure with the wrong number
of arguments, wouldn't both situations result in weird runtime errors?

On 12/10/10 22:34, Armando Blancas wrote:
>> Back to my question: Am I trying to do Java in Clojure? Is there a more
>> Lisp-y way to do this?
> 
> You can hide the types so your client code is more lispy:
> (defn load-page [prov] (.loadPage prov))
> ;;test
> (def mp (make-mock-provider)) ... (load-page mp)
> ;;production
> (def prov (make-provider)) ... (load-page prov)
> 
> Depending on your app the provider could be a singleton and need not
> be passed to each function. Another option is multimethods, in which
> case you'd be using mock functions with an argument that would
> indicate which version to dispatch to.
> 
> As for the repl, I think it works just as well for bottom-up and top-
> down development. I use it for both all the time and to avoid throw-
> away tests I write them top-down, black-box for only what's visible to
> client/interop code first, then move down the layers as the code is
> more mature and stable. I'm not really into TDD but I depend on a test
> suite as complete as I can get it.
> 




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Re: precise numbers

[Jarl Haggerty]

A slight tangent, is there anyway to represent exact square roots?
I'd like to have an exact closed form fibonacci function.

On Oct 13, 1:28 pm, David Sletten  wrote:
> On Oct 12, 2010, at 5:44 PM, Brian Hurt wrote:
>
> >   For example, in base 10, 1/3 * 3 = 0.9...  
>
> It may seem counterintuitive, but that statement is perfectly true.
> 1 = 0....
>
> That's a good test of how well you understand infinity.
>
> Of course, the problem arises when we truncate the string of 9's, which we 
> must invariably do in a computer-based representation.
>
> Have all good days,
> David Sletten

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Re: precise numbers

[Alan]

Um, not if you're going to try and turn them into numbers first. But
if you store them as ['sqrt 5] or some similar operator/operand pair,
then you can manipulate them symbolically and wait for them to cancel
out, instead of evaluating them. This requires implementing some kind
of symbolic-algebra system, but it's certainly possible: when I was in
college my TI-89 could compute the closed form for arbitrarily large N
without losing precision (or accuracy).

On Oct 13, 2:02 pm, Jarl Haggerty  wrote:
> A slight tangent, is there anyway to represent exact square roots?
> I'd like to have an exact closed form fibonacci function.
>
> On Oct 13, 1:28 pm, David Sletten  wrote:
>
> > On Oct 12, 2010, at 5:44 PM, Brian Hurt wrote:
>
> > >   For example, in base 10, 1/3 * 3 = 0.9...  
>
> > It may seem counterintuitive, but that statement is perfectly true.
> > 1 = 0....
>
> > That's a good test of how well you understand infinity.
>
> > Of course, the problem arises when we truncate the string of 9's, which we 
> > must invariably do in a computer-based representation.
>
> > Have all good days,
> > David Sletten
>
>

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Re: Override print-method of struct

[Laurent PETIT]

You can add a :type metadata to your maps, and this can be catched by the
(type) method of multimethods.

But if you have parent -> child -> parent -> child ... relationships, I
guess that you're building a tree made of mixins of maps and refs to maps
... and indeed this should bell some rings in your head if you haven't
already carefully balanced alternative choices ...

2010/10/13 andrei 

> How can I override print-method for a map, defined with defstruct?
>
> I have to create object hierarchy: one map is a parent for another,
> i.e. it holds link to a child, and another is a child for the first
> one, i.e. holds link to a parent. When I try to print it, I get
> StackOverflowError since printer tries recursively print objects:
>
>  parent -> child -> parent -> child -> 
>
> The best solution I see is to override print-method or str, so the
> printing will go normally. I found this topic:
>
>
> http://groups.google.com/group/clojure/browse_thread/thread/4a675222f208899d
>
> which shows how to override print-method for objects defined by
> deftype, but is there a way to do same trick for maps? Maybe it is
> possible to add some special tag to object's meta? Or to redefine
> print-method in the only namespace?
>
> Or maybe I'm just looking at the wrong direction?
>
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Re: Creating a new library

[Vilson Vieira]

Thank you guys about all the valuable answers.

I've pushed the jars to Clojars on my group [1] and updated the wiki with a
simple tutorial on how to create a POM to non-clojure jars [2].

All the best.

[1] http://clojars.org/groups/org.clojars.automata
[2] http://github.com/ato/clojars-web/wiki/POM

2010/10/13 

> I need a new pair of eyes...
>
> Saul Hazledine  wrote ..
> > On Oct 13, 1:21 pm, lprefonta...@softaddicts.ca wrote:
> > > Good to know... is this written somewhere ? I looked at Clojars
> yesterday
> > > but did not find anything...
> > >
> >
> > Its mentioned near the end of the tutorial:
> >   http://github.com/ato/clojars-web/wiki/tutorial
> >
> > Saul
> >
> > --
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Re: Is ClojureCLR converging toward a release?

[eyeris]

Thank you for all the work you've put into this!


On Oct 11, 5:39 pm, dmiller  wrote:
> Check out the downloads area onhttp://github.com/richhickey/clojure-clr.
> Grabclojure-clr-1.2.0.zip.  Unzip, start up Clojure.Main.exe and you
> should be running.  The zip also contains Clojure.Compile.exe, which
> you can invoke with command line arguments indicating files to
> compile.  The support DLLs for the DLR are included.  These are debug
> builds for .Net 3.5 only.
>
> Within the next day or so, the master branch will updated with a new
> build process that will create debug and release builds for 3.5 and
> 4.0.  Futurebinarydistributions will be available in all four
> flavors.
>
> The new build process and extension to .Net 4.0  requires 
> theClojureCLRproject to move to Visual Studio 2010.  It will simplify
> getting started for developers, too.   It's ready to go.  I just have
> to get the wiki pages updated.
>
> -David
>
> On Oct 4, 11:13 pm, Mike K  wrote:
>
> > David, Rich: any further updates on this?
>
> >    Mike
>
> > On Sep 24, 8:24 am, dmiller  wrote:
>
> > >  Just waiting for that person's CA to be processed by Rich.

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Re: precise numbers

[Felix H. Dahlke]

On 13/10/10 22:28, David Sletten wrote:
> 
> On Oct 12, 2010, at 5:44 PM, Brian Hurt wrote:
> 
>>   For example, in base 10, 1/3 * 3 = 0.9...  
> 
> It may seem counterintuitive, but that statement is perfectly true.
> 1 = 0....
> 
> That's a good test of how well you understand infinity.

I'm clearly not a mathematician, but doesn't 0.9... asymptotically
approach 1, i.e. never reaching it? How is that the same as 1?



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Re: precise numbers

[Matt Fowles]

Felix~

You are correct that the sequence of numbers

0.9
0.99
0.999
...

asymptotically approaches 1; however, the number 0.... (with an infinite
number of 9s) is equal to 1.  The formal proof of this is fairly tricky as
the definition of the real number is usually done as an equivalence class of
Cauchy sequences; a simplified version of the proof can be thought of as
follows:

For any two real numbers *a* and *b* there exists an infinite number of real
numbers *c *such that *a < c < b*.  However, there do not exist any numbers
between 0.9... and 1, thus they must be same number.

As it turns out, it took mathematicians a long time to nail down formally
exactly what we naively think of as "numbers".

Matt

On Wed, Oct 13, 2010 at 6:27 PM, Felix H. Dahlke  wrote:

> On 13/10/10 22:28, David Sletten wrote:
> >
> > On Oct 12, 2010, at 5:44 PM, Brian Hurt wrote:
> >
> >>   For example, in base 10, 1/3 * 3 = 0.9...
> >
> > It may seem counterintuitive, but that statement is perfectly true.
> > 1 = 0....
> >
> > That's a good test of how well you understand infinity.
>
> I'm clearly not a mathematician, but doesn't 0.9... asymptotically
> approach 1, i.e. never reaching it? How is that the same as 1?
>
>

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Re: precise numbers

[David Sletten]

Here's a slightly more informal argument. Suppose you challenge me that 1 is 
not equal to 0.... What you are saying is that 1 - 0.... is not equal 
to 0, i.e., the difference is more than 0. But for any positive value 
arbitrarily close to 0 I can show that 0.999... is closer to 1 than that. If 
you were to say that the difference is 0.1, I could show that 0.999... > 0.9 so 
the difference is smaller. For every 0 you added to your challenge: 0.1, 0.01, 
0.001 I could provide a counterexample with another 9: 0.9, 0.99, 0.999, ... In 
other words, there is no positive number that satisfies your claim, so equality 
must hold.

Have all good days,
David Sletten

On Oct 13, 2010, at 6:36 PM, Matt Fowles wrote:

> Felix~
> 
> You are correct that the sequence of numbers
> 
> 0.9
> 0.99
> 0.999
> ...
> 
> asymptotically approaches 1; however, the number 0.... (with an infinite 
> number of 9s) is equal to 1.  The formal proof of this is fairly tricky as 
> the definition of the real number is usually done as an equivalence class of 
> Cauchy sequences; a simplified version of the proof can be thought of as 
> follows:
> 
> For any two real numbers a and b there exists an infinite number of real 
> numbers c such that a < c < b.  However, there do not exist any numbers 
> between 0.9... and 1, thus they must be same number.
> 
> As it turns out, it took mathematicians a long time to nail down formally 
> exactly what we naively think of as "numbers".
> 
> Matt
> 
> On Wed, Oct 13, 2010 at 6:27 PM, Felix H. Dahlke  wrote:
> On 13/10/10 22:28, David Sletten wrote:
> >
> > On Oct 12, 2010, at 5:44 PM, Brian Hurt wrote:
> >
> >>   For example, in base 10, 1/3 * 3 = 0.9...
> >
> > It may seem counterintuitive, but that statement is perfectly true.
> > 1 = 0....
> >
> > That's a good test of how well you understand infinity.
> 
> I'm clearly not a mathematician, but doesn't 0.9... asymptotically
> approach 1, i.e. never reaching it? How is that the same as 1?
> 
> 
> 
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Re: precise numbers

[Mike Meyer]

On Thu, 14 Oct 2010 00:27:39 +0200
"Felix H. Dahlke"  wrote:

> On 13/10/10 22:28, David Sletten wrote:
> > 
> > On Oct 12, 2010, at 5:44 PM, Brian Hurt wrote:
> > 
> >>   For example, in base 10, 1/3 * 3 = 0.9...  
> > 
> > It may seem counterintuitive, but that statement is perfectly true.
> > 1 = 0....
> > 
> > That's a good test of how well you understand infinity.
> 
> I'm clearly not a mathematician, but doesn't 0.9... asymptotically
> approach 1, i.e. never reaching it? How is that the same as 1?

This representation implies the sum of the series (iterate #(/ % 10)
9/10), and that sum behaves as you say. However, since the series is
infinite, you can prove that the number it represents is actually
equal to one, like so:

1) a = 0.999... # define a as 0.999...
2) 10a = 9.999...   # multiply both sides by 10
3) 10a - a = 9.999... - 0.999...# subtract equation 1 from equation 2
4) 9a = 9   # simplify
5) a = 1# divide both sides by 9.

The subtraction step doesn't work unless the sequence is infinite, if
a is any finite sequence of 9s, you'll get a number whose decimal
representation is matches the re 8\.(9)*1. This relies on the property
that adding 1 to an infinite number gives you back the same infinite
number, so that:

(= (rest (map #(* % 10) (iterate #(/ % 10) 9/10)))
   (iterate #(/ % 10) 9/10))

is true, but I don't recommend typing that into a repl to check it!

Hmm. I wonder if you could represent irrationals as lazy sequences,
and do arithmetic on those?

http://www.mired.org/consulting.html
Independent Network/Unix/Perforce consultant, email for more information.

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Re: precise numbers

[Terrance Davis]

The quick and dirty proof (not formal proof) for 1 = ....

1/3 = .33...
2/3 = .66...
3/3 = .99...

Think of 3/3 as 1/3 (that is .3...) times 3.

-Terrance Davis
www.terrancedavis.com



Felix H. Dahlke wrote:

On 13/10/10 22:28, David Sletten wrote:
  

On Oct 12, 2010, at 5:44 PM, Brian Hurt wrote:


  For example, in base 10, 1/3 * 3 = 0.9...  
  

It may seem counterintuitive, but that statement is perfectly true.
1 = 0....

That's a good test of how well you understand infinity.



I'm clearly not a mathematician, but doesn't 0.9... asymptotically
approach 1, i.e. never reaching it? How is that the same as 1?

  


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Re: Override print-method of struct

[andrei]

That works, thanks!

Yeah, I understand that it is not the best data structure to use. The
task is to create a tree, and it is needed to get all children and all
parents of specified node in this tree in a constant time. So, I
cannot see another way to do it except storing refs both from parents
to children and from children to parents.

On Oct 14, 12:40 am, Laurent PETIT  wrote:
> You can add a :type metadata to your maps, and this can be catched by the
> (type) method of multimethods.
>
> But if you have parent -> child -> parent -> child ... relationships, I
> guess that you're building a tree made of mixins of maps and refs to maps
> ... and indeed this should bell some rings in your head if you haven't
> already carefully balanced alternative choices ...
>
> 2010/10/13 andrei 
>
> > How can I override print-method for a map, defined with defstruct?
>
> > I have to create object hierarchy: one map is a parent for another,
> > i.e. it holds link to a child, and another is a child for the first
> > one, i.e. holds link to a parent. When I try to print it, I get
> > StackOverflowError since printer tries recursively print objects:
>
> >  parent -> child -> parent -> child -> 
>
> > The best solution I see is to override print-method or str, so the
> > printing will go normally. I found this topic:
>
> >http://groups.google.com/group/clojure/browse_thread/thread/4a675222f...
>
> > which shows how to override print-method for objects defined by
> > deftype, but is there a way to do same trick for maps? Maybe it is
> > possible to add some special tag to object's meta? Or to redefine
> > print-method in the only namespace?
>
> > Or maybe I'm just looking at the wrong direction?
>
> > --
> > You received this message because you are subscribed to the Google
> > Groups "Clojure" group.
> > To post to this group, send email to clojure@googlegroups.com
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Re: Override print-method of struct

[meb]

Instead of using a ref, you might consider using a closure, which
seems a little more functional.

So every child would simply store a function that when called would
return the map of the parent, map you capture using a closure.  This
would also reduce your printing problems because functions just print
their classname, and you would know that the function brings you back
to the parent.

I did this for a Neo4j wrapper I wrote to idiomatically represent
traversing webs and trees.

Would that help anyway?  Then you wouldn't have to worry about messing
with redefining prints or using alters.  The thunk would be created as
part of the process.

Mark

On Oct 13, 4:21 pm, andrei  wrote:
> That works, thanks!
>
> Yeah, I understand that it is not the best data structure to use. The
> task is to create a tree, and it is needed to get all children and all
> parents of specified node in this tree in a constant time. So, I
> cannot see another way to do it except storing refs both from parents
> to children and from children to parents.
>
> On Oct 14, 12:40 am, Laurent PETIT  wrote:
>
>
>
> > You can add a :type metadata to your maps, and this can be catched by the
> > (type) method of multimethods.
>
> > But if you have parent -> child -> parent -> child ... relationships, I
> > guess that you're building a tree made of mixins of maps and refs to maps
> > ... and indeed this should bell some rings in your head if you haven't
> > already carefully balanced alternative choices ...
>
> > 2010/10/13 andrei 
>
> > > How can I override print-method for a map, defined with defstruct?
>
> > > I have to create object hierarchy: one map is a parent for another,
> > > i.e. it holds link to a child, and another is a child for the first
> > > one, i.e. holds link to a parent. When I try to print it, I get
> > > StackOverflowError since printer tries recursively print objects:
>
> > >  parent -> child -> parent -> child -> 
>
> > > The best solution I see is to override print-method or str, so the
> > > printing will go normally. I found this topic:
>
> > >http://groups.google.com/group/clojure/browse_thread/thread/4a675222f...
>
> > > which shows how to override print-method for objects defined by
> > > deftype, but is there a way to do same trick for maps? Maybe it is
> > > possible to add some special tag to object's meta? Or to redefine
> > > print-method in the only namespace?
>
> > > Or maybe I'm just looking at the wrong direction?
>
> > > --
> > > You received this message because you are subscribed to the Google
> > > Groups "Clojure" group.
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> > > Note that posts from new members are moderated - please be patient with
> > > your first post.
> > > To unsubscribe from this group, send email to
> > > clojure+unsubscr...@googlegroups.com > >  >
> > > For more options, visit this group at
> > >http://groups.google.com/group/clojure?hl=en

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Re: Help to optimize palindrome search from input file

[Btsai]

I think the indexing in all-combs may be off, causing it to miss
certain combinations/substrings.

user=> (all-combs "abc")
("a" "ab")

I used this instead:

(defn substrings [s]
  (let [length (count s)]
(for [i (range length)
  j (range (inc i) (inc length))]
  (subs s i j

user=> (substrings "abc")
("a" "ab" "abc" "b" "bc" "c")

On Oct 12, 1:02 pm, tonyl  wrote:
> Hi, I just started to learn clojure in a more serious way and I am
> doing the first level of the greplin challenge.
>
> I made it to work with a short palindrome like the example they give
> me, but when it comes to work with the input file, it takes for ever
> and I have to stop it.
>
> $ time clj level1.clj
> ^C
> real    11m35.477s
> user    1m44.431s
> sys     9m3.878s
>
> This is my code:
>
> (defn palindrome? [s]
>   (= s (reduce str (reverse s
>
> (defn all-combs [in]
>   (let [len (count in)]
>     (for [i (range 0 (- len 2)), j (range (+ i 1) len)]
>       (subs in i j
>
> (defn max-comp [x y]
>   (let [lenx (count x), leny (count y)]
>     (cond (< lenx leny) 1
>           (= lenx leny) 0
>           (> lenx leny) -1)))
>
> ;;(let [input "I like racecars that go fast"]
> (let [input (slurp "../_input/level1.in")]
>     (println (nth (sort max-comp (filter palindrome? (all-combs
> input))) 0)))
>
> The input file is thishttp://challenge.greplin.com/static/gettysburg.txt
>
> It looks a bit procedural. It is long, but I don't think is the
> biggest bottleneck, I think it is my approach to create all the
> combinations possible for substrings. Maybe I should be using a lazy
> seq? How would I go to do that?

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Re: Test-driven development in Clojure

[Armando Blancas]

One thing that OOP and FP can have in common is the use of
polymorphism. With protocols and types you can implement your Java
design efficiently because you'll get basically the same interfaces
and classes. The thing about hiding the calls to instances of a data
type is only to make the client code not reply on the interop
notation, even if it is only to call a method on them, just like
Clojure core functions do.

With multimethods you can have different versions of the same
function. You're right, you call it with the necessary data, one of
which will be the one that controls the dispatch. Both data types and
multimethods provide late-binding; the difference is that multi-
methods are objects turned inside-out, as if you keep a reference to
this (as a record with fields) and use in function calls. And each
method is a particular responsibility. That's how I think about it,
anyway.

Either choice should be fine. I write Java interfaces for
implementations in Clojure when I want interop with Java, otherwise I
use multimethods and do it all in Clojure.

On Oct 13, 1:37 pm, "Felix H. Dahlke"  wrote:
> I see. So instead of using interfaces and implementations of these, I
> would simply use closures, one for mock and one for production? That was
> actually my first attempt, but I didn't like it back then.
>
> Take this code for example - passing a function just to have it called
> feels weird:
>
> (defn load-page [provider name]
>   (provider name))
>
> (load-page (make-mock-provider) "home")
>
> In Java, this would probably look like this:
>
> class PageLoader {
>     Provider provider;
>
>     PageLoader(Provider p) {
>         provider = p;
>     }
>
>     Page loadPage(String name) {
>         provider.loadPage(name);
>     }
>
> }
>
> PageLoader l = new PageLoader(new MockProvider());
> l.loadPage("home");
>
> Then again, it might just feel weird because I've gotten very used to
> OOP. In my Java code, loading pages is a responsibility of the
> PageLoader and it delegates it to the Provider. Objects have
> responsibilities and send messages to each other to fulfill these,
> that's OOP.
>
> In functional programming, there's simply a function that has a certain
> functionality, and everything it needs to fulfill it has to be provided
> by the caller. That's at least how I understand it by now.
>
> Maybe I should just call the function returned by (make-mock-provider)
> directly? The interface in Java has the great benefit of ensuring type
> safety (plus there's no closures yet, so it's the only way), but does
> this make sense in a dynamic language? I mean, if I passed an
> implementation of the wrong interface or a closure with the wrong number
> of arguments, wouldn't both situations result in weird runtime errors?
>
> On 12/10/10 22:34, Armando Blancas wrote:
>
> >> Back to my question: Am I trying to do Java in Clojure? Is there a more
> >> Lisp-y way to do this?
>
> > You can hide the types so your client code is more lispy:
> > (defn load-page [prov] (.loadPage prov))
> > ;;test
> > (def mp (make-mock-provider)) ... (load-page mp)
> > ;;production
> > (def prov (make-provider)) ... (load-page prov)
>
> > Depending on your app the provider could be a singleton and need not
> > be passed to each function. Another option is multimethods, in which
> > case you'd be using mock functions with an argument that would
> > indicate which version to dispatch to.
>
> > As for the repl, I think it works just as well for bottom-up and top-
> > down development. I use it for both all the time and to avoid throw-
> > away tests I write them top-down, black-box for only what's visible to
> > client/interop code first, then move down the layers as the code is
> > more mature and stable. I'm not really into TDD but I depend on a test
> > suite as complete as I can get it.
>
>
>
>  signature.asc
> < 1KViewDownload

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Re: Is ClojureCLR converging toward a release?

[Miki]

What's the status on Mono?

On Oct 11, 3:39 pm, dmiller  wrote:
> Check out the downloads area onhttp://github.com/richhickey/clojure-clr.
> Grab clojure-clr-1.2.0.zip.  Unzip, start up Clojure.Main.exe and you
> should be running.  The zip also contains Clojure.Compile.exe, which
> you can invoke with command line arguments indicating files to
> compile.  The support DLLs for the DLR are included.  These are debug
> builds for .Net 3.5 only.
>
> Within the next day or so, the master branch will updated with a new
> build process that will create debug and release builds for 3.5 and
> 4.0.  Future binary distributions will be available in all four
> flavors.
>
> The new build process and extension to .Net 4.0  requires the
> ClojureCLR project to move to Visual Studio 2010.  It will simplify
> getting started for developers, too.   It's ready to go.  I just have
> to get the wiki pages updated.
>
> -David
>
> On Oct 4, 11:13 pm, Mike K  wrote:
>
> > David, Rich: any further updates on this?
>
> >    Mike
>
> > On Sep 24, 8:24 am, dmiller  wrote:
>
> > >  Just waiting for that person's CA to be processed by Rich.

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Re: precise numbers

[Felix H. Dahlke]

OKay, I think I get it. Thanks :)

On 14/10/10 00:56, David Sletten wrote:
> Here's a slightly more informal argument. Suppose you challenge me that
> 1 is not equal to 0.... What you are saying is that 1 - 0.... is
> not equal to 0, i.e., the difference is more than 0. But for any
> positive value arbitrarily close to 0 I can show that 0.999... is closer
> to 1 than that. If you were to say that the difference is 0.1, I could
> show that 0.999... > 0.9 so the difference is smaller. For every 0 you
> added to your challenge: 0.1, 0.01, 0.001 I could provide a
> counterexample with another 9: 0.9, 0.99, 0.999, ... In other words,
> there is no positive number that satisfies your claim, so equality must
> hold.
> 
> Have all good days,
> David Sletten
> 
> On Oct 13, 2010, at 6:36 PM, Matt Fowles wrote:
> 
>> Felix~
>>
>> You are correct that the sequence of numbers
>>
>> 0.9
>> 0.99
>> 0.999
>> ...
>>
>> asymptotically approaches 1; however, the number 0.... (with an
>> infinite number of 9s) is equal to 1.  The formal proof of this is
>> fairly tricky as the definition of the real number is usually done as
>> an equivalence class of Cauchy sequences; a simplified version of the
>> proof can be thought of as follows:
>>
>> For any two real numbers /a/ and /b/ there exists an infinite number
>> of real numbers /c /such that /a < c < b/.  However, there do not
>> exist any numbers between 0.9... and 1, thus they must be same number.
>>
>> As it turns out, it took mathematicians a long time to nail down
>> formally exactly what we naively think of as "numbers".
>>
>> Matt
>>
>> On Wed, Oct 13, 2010 at 6:27 PM, Felix H. Dahlke > > wrote:
>>
>> On 13/10/10 22:28, David Sletten wrote:
>> >
>> > On Oct 12, 2010, at 5:44 PM, Brian Hurt wrote:
>> >
>> >>   For example, in base 10, 1/3 * 3 = 0.9...
>> >
>> > It may seem counterintuitive, but that statement is perfectly true.
>> > 1 = 0....
>> >
>> > That's a good test of how well you understand infinity.
>>
>> I'm clearly not a mathematician, but doesn't 0.9... asymptotically
>> approach 1, i.e. never reaching it? How is that the same as 1?
>>
>>
>>
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> 
> 
> 
> 
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