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### Re: Spooky math problem

by ikegami (Pope)
 on Mar 25, 2009 at 04:31 UTC ( #753010=note: print w/replies, xml ) Need Help??

in reply to Spooky math problem

One flaw: The guarantee fails if the enveloper contains two adjacent numbers. 50% + 0.5 * 0 is not greater than 50%.

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Re^2: Spooky math problem
by tilly (Archbishop) on Mar 25, 2009 at 12:49 UTC
In standard mathematics there is no such thing as adjacent real numbers. Endless arguments from non-mathematicians notwithstanding, 1 and 0.999... are two different ways of representing the same number and not two different numbers.

This is because one of the rules the real numbers follow is trichotomy, which says that if x and y are real numbers then exactly one of the statements x-y>0, x=y and y-x>0 must be true. (Depending on the axiomatization chosen trichotomy can be either an axiom or a theorem. Either way it is true.) The requirement in the problem that the numbers be different rules out the second possibility.

In fact we can make an even stronger statement. There is a basic theorem (called the Archimedean principle) which makes an even stronger assertion, given any two distinct reals there is always a rational number between them. So let n/m be a rational number between 0 and x-y. Then x and y must differ by more than 1/m. So you see that between any two real numbers there is always a finite visible gap. There is therefore no such thing as an infinitesmal in the standard real number system.

(Google will provide adequate references to demonstrate that I'm not just making this up.)

(Google will provide adequate references to demonstrate that I'm not just making this up.)
You hacked google to become a reference so it would appear that way ... ;P

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 [1nickt]: choroba Understood. I'm wondering about the logic in a cpanfile. If the perl doesn't support threads, it's easy: require MCE. If the perl does support threads, as you say the user has a choice, so require both? Or, assume that irrespective of the choide [1nickt]: ... choice, the threaded-perl user *probably* wants to use threads, therefore only require threads and leave MCE out, allowing the user to manually install if desired? [choroba]: just require any of MCE and threads. Not sure if that's possible in the cpanfile, but should be possible early in the Makefile [1nickt]: The app expects threads as default anyway, right? [choroba]: that's true [1nickt]: expects threads *to be* the default [1nickt]: I think cpanfile can handle the logic. testing now.

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