If your definition of a mathematical decimal number is 'one that when written in decimal has a decimal point in it', do you want the answer 'true' or 'false' for the floating point number 1.0? I don't see how that definition of decimal number makes a lot of sense, or why you would want a function that tells you that.
If you want a function that tells you 'can this number be represented exactly as an integer?', then perhaps something like (== x (convert-to-nearest-BigInteger x)), but I am not sure off hand a good way to write convert-to-nearest-BigInteger. According to one answer to this StackOverflow question, converting a double or float to BigDecimal first, then to the nearest BigInteger, may work: http://stackoverflow.com/questions/17960186/is-there-anyway-to-convert-from-double-to-biginteger Andy On Mon, Jun 15, 2015 at 10:44 AM, John Gabriele <jmg3...@gmail.com> wrote: > Thanks for the clarifications, all. Had not thought about exact vs. > inexact results. > > Also, I see that --- if I simply want to know if a number is a > (mathematical) decimal number, I can just do `(or (float? x) (decimal? x))`. > > -- John > > > > > On Friday, June 12, 2015 at 12:08:56 PM UTC-4, Gary Verhaegen wrote: >> >> Your definitions are correct, but in a different domain: you are using >> the mathematical definitions. >> >> What these functions give you is information about the representation of >> the numbers in memory, not information about the numbers themselves. For >> example, (integer? 1.0) will give you false. >> >> A rational number in mathematics is one that can be written as a fraction >> (of integers), or equivalently one that does not have an infinite and >> non-periodic expansion. A rational number in the sense of "rational?" in >> Clojure is an object in memory which is actually stored as a couple of >> integers, not merely a valie that could be stored that way. >> >> As others have mentioned, the way in which a number is stored will have >> some impact on how much memory it takes up, how fast the computer can >> compute operations on it, and how much precision will be lost with these >> operations. >> >> As always, Clojure puts more emphasis on behaviours and interfaces than >> on implementations, so you should really understand "rational?" as "will I >> get an exact answer if I use operations that would give an exact answer >> with a rational number (in the mathematical sense)?" >> >> For example, (/ 1M 3) will throw an exception rather than returning an >> inexact, truncated answer, whereas (/ 1.0 3) will happily lie to you. >> (According to the documentation, BigDecimal always returns a correct value >> or throws an exception, except if you explicitly tell it to round. It can >> represent values down to about 1e-2_147_483_647, and up to filling your >> computer's memory.) >> >> For a first step towards understanding floating-point values, I would >> recommend reading: >> >> >> http://blog.reverberate.org/2014/09/what-every-computer-programmer-should.html >> >> On Friday, 12 June 2015, John Gabriele <jmg3...@gmail.com> wrote: >> >>> My understanding is that a rational number is one that can be written as >>> a fraction. For example, 5.1, which can be written as 51/10. But Clojure >>> seems to disagree: >>> >>> ~~~ >>> (rational? 51/10) ;=> true >>> (rational? 5.1) ;=> false (?!) >>> ~~~ >>> >>> Is my definition of "rational" incorrect? >>> >>> Also, my understanding is that a decimal number is one that has a >>> decimal point in it, like, for example, 5.1. However: >>> >>> ~~~ >>> (decimal? 5.1) ;=> false (?!) >>> ~~~ >>> >>> And while typing this, I also notice that while `integer?` acts like I'd >>> expect, `float?` does something weird: >>> >>> ~~~ >>> (integer? 5) ;=> true Yes >>> (integer? 5N) ;=> true Yes >>> (integer? 5.1) ;=> false >>> >>> (float? 5.1) ;=> true >>> (float? 5.1M) ;=> false (?!) >>> ~~~ >>> >>> Maybe I'm confusing "floating point number" with "decimal number" here? >>> If so, what's the difference? >>> >>> Thanks! >>> >>> -- >>> 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 >>> 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 >>> --- >>> You received this message because you are subscribed to the Google >>> Groups "Clojure" group. >>> To unsubscribe from this group and stop receiving emails from it, send >>> an email to clojure+unsubscr...@googlegroups.com. >>> For more options, visit https://groups.google.com/d/optout. >>> >> -- > 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 > 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 > --- > You received this message because you are subscribed to the Google Groups > "Clojure" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to clojure+unsubscr...@googlegroups.com. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "Clojure" group. 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