[Mono-list] Native number types but not general number type?
Edward Ned Harvey (mono)
edward.harvey.mono at clevertrove.com
Wed Feb 25 14:08:52 UTC 2015
> From: mono-list-bounces at lists.ximian.com [mailto:mono-list-
> bounces at lists.ximian.com] On Behalf Of Michael McGlothlin
> Likewise I'd like to more easily use lossless numbers of unlimited size,
> including fractional values,
You might have better luck with a specific question, but in general, what you're asking is impossible. For example, how can you losslessly represent 1/3, or pi?
Well, if you're using base-3, you could losslessly represent 1/3 as 0.1, but in base-2 or base-10, it's an infinitely repeating number. So let there be an arbitrary-base number system with arbitrary precision... Now what if you take base-3 (0.1) and multiply it by base-7 (0.1), the lossless result is base-21 (0.1). Which brings up a new question - base-21 (0.1) multiplied by 20 is 20/21, so how do you represent that? For hex base-16, we can go up to F to represent 15, so I guess in base-21, we could go up to L, but for arbitrary-base, you could have infinite numbers to represent the first column. For example, the number 1,000,000 (decimal) could be equally represented as base-1,000,000 (1). It would work (inefficiently, with lots of ambiguity and wrangling) as long as every number could be represented in rational form.
So then you're stuck being unable to represent irrational numbers... Such as e and pi....
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