Re: factorial and exponent


"Richard Heathfield" <rjh@xxxxxxxxxxxxxxx> ha scritto nel messaggio news:A5qdnVfG0vFws-jbnZ2dnUVZ8rKdnZ2d@xxxxxxxxx
Army1987 said:
"Richard Heathfield" <rjh@xxxxxxxxxxxxxxx> ha scritto nel messaggio
news:Gv6dnQ2-P8SDeunbnZ2dnUVZ8t_inZ2d@xxxxxxxxx
BiGYaN said:
<snip>

Use GMP library found in http://gmplib.org/
It will enable you to do "Arithmetic without Limitations" !!

Nonsense.

Consider an integer greater than or equal to 2. Call it A. Consider
another integer greater than or equal to 2. Call it B.

Raise A to the power B, storing the result in A. Now raise B to the
power A, storing the result in B. If you repeat this often enough,
you *will* hit a limit, no matter what numerical library you use.

But it is a limit of your computer, not of the library itself.

Nevertheless, it is a limit, and therefore the library *cannot* 'enable
you to do "Arithmetic without Limitations"', and therefore BiGYaN's
statement is nonsense.
If you cannot compute a number n with a computer, you can always
(at least in principle) use a computer with a larger size_t and
compute it.
Your statement is much like "You cannot use the long division
algorithm indefinitely because sooner or later you'll run out of
paper", or "There is a N such as you cannot draw a regular
(2^N * 3 * 5 * 17 * 257 * 65537)-gon with straightedge and compass,
because even if the polygon were as large as the universe, each
side would need to be shorter than a Planck length".
The library does enable Arithmetic without Limitations. It is the
implementation (and the universe) which put the limits.


.

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