Re: infinity

Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> writes:

> Ho hum? The set of naturals is the set of all consecutive finite
> whole numbers starting from 1. The proof shows that for any such
> set,

Hand-waving hogwash again. There is only _one_ set of all consecutive
finite whole numbers starting from 1. But there is an infinite number
of finite set of consecutive finite whole numbers starting with 1.
The set of _all_ consecutive finite whole numbers is not one of them.

> the size of the set is a member of the set.

Of all finite sets of consecutive whole numbers starting with 1. But
the set of _all_ consecutive whole numbers starting with 1 is not one
of them.

> Do you know what the largest finite natural is? No.

It is trivial to show that such a number does not exist.

> Do you know what the size of the set of finite naturals is?

It is trivial to show by induction that it can't be a finite natural.

> No. But, you know those two numbers are the same number,

Guffaw.

> so one cannot be finite while the other is infinite.

One does not exist, and the other is not a finite number. There are
frameworks in which it is a particular infinite number, though, that
labels the equivalence class containing the set of natural numbers as
one as its elements.

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
.

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