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Topic: Discussion with WM - Frustration reaches boiling point (What
is not clear?)

Replies: 8   Last Post: Jul 5, 2014 11:16 PM

 Messages: [ Previous | Next ]
 ross.finlayson@gmail.com Posts: 2,720 Registered: 2/15/09
Re: Discussion with WM - Frustration reaches boiling point (What
is not clear?)

Posted: Jul 5, 2014 2:00 PM

On 7/5/2014 10:48 AM, PotatoSauce wrote:
> On Saturday, July 5, 2014 1:34:21 PM UTC-4, muec...@rz.fh-augsburg.de wrote:
>> On Saturday, 5 July 2014 17:14:53 UTC+2, PotatoSauce wrote:
>>
>>
>>
>>
>>

>>>
>>
>>> If you are assuming from the start N doesn't exist
>>
>>
>>
>> I do not.
>>
>>
>>

>>> to prove that there is no bijection between N and Q, then your logic is entirely off.
>>
>>
>>
>> I assume N to exist and to enumerate all rational numbers. Only mathematical reality of real analysis contradicts this assumption. That is called a proof by contradiction.
>>

>>>
>>
>>>
>>
>>>
>>
>>> You want lim card(s_n) to represent the cardinality of the sequence s_n "at infinity."
>>
>>
>>
>> I do not assume that a limit exists. But I show that the sets cannot get empty even if a limit exist.
>>

>
> But you agreed that
>
> lim t->0 (-t,0) u (0, t) = { }.
>
> You have also tacitly acknowledged that set limits pass through set relation, thus
>
> {} <= lim t->0 { t/2 } <= lim t-> 0 (-t,0) u (0, t) = {}
>
> (using <= for subset)
>
> So clearly, we can have non-empty sets with empty limit sets.
>
>
>

And so clearly the other way?

You can see from topology
running out either, I would hope.

Would you agree that there are
definitions in topology? At all?