Re: infinity

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

> stephen@xxxxxxxxxx said:
>>
>> > Your insistence that there are an infinite number of finite
>> > strings is a consequence of believing that there are an infinite
>> > number of finite naturals,
>> Which there are, and which I can prove.
>
> No, I have proven quite the opposite. It is obvious that no set of
> naturals can have a set size larger than its largest element.

No set of naturals with a last element.

>> Your inductive proofs are always wrong. You prove that
>> every set of the form {1, 2, ... n} has a maximum element
>> and that the size of the set equals the maximum element.
>> However, the set { 1, 2, ... } is not a set of that
>> form, so your proof does not apply to it.

> Because there is no largest finite, the proof is invalid?

Quite so.

> What a typical stupid response.

What a typical response to stupidity, rather.

> It has been proven that NO n in N has an infinite number of
> predecessors,

Correct.

> therefore the set cannot contain an infinite number of members.

Whining does not make it so. "therefore" can't be placed between
arbitrary unconnected sentences and be expected to result in a valid
argument.

>> As for your contradictions, you have the mistaken idea
>> that aleph_0 is a natural number. It is not.
>
> I have the correct understanding that the size of the set of all
> finite naturals is equal to the largest finite natural, which
> doesn't exist.

Let's rephrase that out of TO-whining: the size of the set of all
finite naturals would be equal to the largest finite natural, if such
a number existed.

There you are: perfectly true, since such a number does not exist.

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

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