Mike Hansen schrieb:
On Mon, Apr 19, 2010 at 11:52 AM, bb <bblo...@arcor.de> wrote:
I get a runtime error, but just would expect infinity! Is there something
wrong or any explanation?
This is because when you do 2^3^4^5 you are computing that number
exactly as an integer, and that number is definitely not infinity. If
you wanted to use floating point arithmetic, then you should start
with something like 2.0:
sage: 2.0^3^4^5
+infinity
Doing something like float(2^3^4^5) computes 2^3^4^5 as an integer and
then tries to convert that to a float.
Also, note that when you type in such an expression, the operations
are done in the following manner:
var(sage: var('x, y, z')
(x, y, z)
sage: x^y^z
x^(y^z)
which is different than
sage: (x^y)^z
(x^y)^z
Since exponentiation is non-associative, you need to be careful with
such differences.
--Mike
Thank you for your answer! I think there is a fundamental question left
apart from the question of assoziativity/non-assoziativity. There Sage
(I think coming from python) does not follow the common rule to evaluate
an expression with operators of the same precedence from left tor right.
Since Georg Cantor there is a difference between countable infinity (in
the actual example) and noncountable infinity ( in the example
calculated with a float). I would not say, that infinity is wrong in
this case, only just because there is existing an infinite set of
integers so that infinity never might be reached. (I think that is the
line of argument of your explanation?) The essential point is, one has
to map the unlimited ideas of math to the restricted possibilities of a
computer.
From a mathamatical point of view one can call the result of the
calculation
sage: 2^(3^(4^5))
---------------------------------------------------------------------------
RuntimeError Traceback (most recent call last)
/home/bb/sage-4.3.5/<ipython console> in <module>()
/home/bb/sage-4.3.5/local/lib/python2.6/site-packages/sage/rings/integer.so
in sage.rings.integer.Integer.__pow__ (sage/rings/integer.c:12114)()
RuntimeError: exponent must be at most 9223372036854775807
sage:
just a bug! Infinity is infinity, if countable or not countable. The
correct math-answer only could be countable infinity! But I think
infinity would in any case be better than "RuntimeError" as an answer!
May be one might introduce a new constant "countable infinity"? Anyway,
I only can recommend the Sage people to catch/raise an exception to
handle that case of an integer overflow of an exponent and avoid the
landing in the mathematical "nirvana" of a RuntimeError. If one thinks
about that problem, one might find that any integer overflow of an
exponent always ends in contable infinity in due consideration of the
computer limits.
Regards BB
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