Am 21.07.2013 01:27, schrieb Warp:
> Kevin Wampler <nob### [at] nowherenet> wrote:
>> Huh?  Certainly infinity isn't an integer/real/rational/etc, but there
>> are consistent and sensible definitions for "number" which include
>> infinity(s) (I'm pretty sure you're aware of this, so maybe I'm missing
>> your point?).
>
> So it's a number that's not any kind of number? It's not an integer,
> it's not rational, it's not irrational, it's not transcendental, and it
> doesn't follow any of the rules of any of the other sets (eg. if you
> add 1 to any number, you get a new number that's larger than the
> original; or if you multiply any number by 0 you get 0.) All mathematical
> operators and functions work completely different for it than for any
> other numbers (moreover, most of them aren't even well-defined for
> infinity.)
>
> Infinity is not a number. It's just a concept that's used to describe
> a more abstract notion. You can use it a bit like if it were a number
> when dealing with things like limits, but even then it's just a shortcut
> notation.

Well, I guess it simply boils down to definitions again: What, actually, 
/is/ a "number" (in the system you're currently examining)?

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