Re: Calculus XOR Probability

Tony Orlow wrote:
Matt Gutting said:
Tony Orlow wrote:

<snip>

Basically, all I'm saying boils down to inductive proof of equality holding for infinite n. If some relationship between measures of a set holds for all finite cases greater than some n, then it can be considered to hold for infinite n,

(Matt)
How do you know that there are any infinite n in the first place?

(Tony again)
Because there are sets with infinite numbers of elements, such as any set of all reals in a finite interval. You cannot have half a real number in your set, so this infinite number is integral, and therefore part of what I consider the integers, or hyperintegers. Otherwise, infinite sets cannot have a size, which makes the "infinite" part kind of meaningless.

But how do you know it's an integer in the first place? In other words, what
makes you so sure that there is an integer describing the size of this set?
Must sizes always be describable by a number? If so, why?

Matt
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