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Topic: ? 534 Finis
Replies: 3   Last Post: Aug 13, 2014 2:48 PM

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Ben Bacarisse

Posts: 1,972
Registered: 7/4/07
Re: ? 534 Finis
Posted: Aug 12, 2014 8:39 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply writes:

> On Tuesday, 12 August 2014 19:09:30 UTC+2, Ben Bacarisse wrote:
>> writes:

>> > On Monday, 11 August 2014 23:00:36 UTC+2, Zeit Geist wrote:
>> >

>> >> Is you Conclusion Not "There is No Bijection between N and Q?
>> >
>> > My conclusion is that all naturals cannot index all rationals.

>> Can you give an example where two sets do index all of each other?

> Yes, of course. Two finite sets of equal cardinality.

>> If it is possible, in WMaths, for finite sets, and the indexing is
>> proved via a one-to-one correspondence (a bijection), what is the
>> difference between these finite bijections and the infinite ones (like
>> those in your book)?

> There is no finished infinity.

You've said this a gazillion times. What you won't say is what this
means. Obviously I knew you'd ignore my question as to whether exists x
c X: not(x c image(f)) because you've painted your self into a corner
with that one, but I did think you might have a go answering the other

| Given, say, a bijection between N and the finite string over the Latin
| alphabet, can you write some formula that is true for this bijection in
| the wrong theory that is set theory, but true in WMaths? (Or vice
| versa, of course.) Maybe it is, in fact, the formula above?

but it seems even this is too risky for you to have a go at answering.
Could it be that you don't know of any formula about such a bijection
that is true in set theory and false in WMaths?

> But as I said already, ask about my proof § 533, in particular what
> according to your inpression is not correct acorsing to classical
> mathematics there.

I have no problem with the theorem in 533.


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