Re: infinity

Jonathan Hoyle <jonhoyle@xxxxxxx> wrote:
>>> 1. If a set is finite, then its size is equal to some finite natural.
>>> 2. For all n, if n is a finite natural, then so is n+1.
>>> 3. For all n, if n is a finite natural, then n+1 > n.
>>> 4. For all n, the set A_{n+1} = { 1, 2, 3, ..., n+1 } has size n+1.
>>> 5. For all n, A_{n+1} is a subset of the set of all finite naturals.
>>> 6. For all X and Y, if X is a subset of Y, then size(X) <= size(Y).
>>> 7. For all x,y and z: if x > y, and y > z, then x > z.
>>> 8. For all x, z: If x > z, then x is not equal to z.

> All 8 statements listed above are true. But so also is the statement:

> 9. There is an infinite number of finite natural numbers.

> That infinite number is, of course, outside the range of finite natural
> numbers and is in fact the first infinite cardinal number Aleph-0.
> Hope that helps!

You should be talking to Tony. You are responding
to people who are asking Tony questions. They already
know what the answers are according to standard definition
and thinking. Tony's thinking however is very nonstandard and
the purpose of the questions is to try and pinpoint down what he
actually thinks.

Stephen
.

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