[OT] How many integers?
rforno at tutopia.com wrote:
> You know, the set of *all* integers (abstract integers, not
> Euphoria nor C nor computer integers) is infinite, but larger than
> the set of *even* integers, that is also infinite.
Actually, the set of even integers (let's call it ZE) and the set of all
integers (Z) are the same size (countably infinite). The standard way
to prove this is to use some function to map from one set to the other,
showing that there is the sets map each other completely with a
one-to-one relationship (bijective):
Then for any z in Z, there is a ze in ZE such that z = ze / 2. In other
words, for any normal integer, I can use even integers to 'count' the
normal integers, and so the sets must be the same size (btw, the set of
rational numbers is the same size, but any interval of real numbers will
be bigger).
Matt Lewis
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