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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 2:32 PM

On 7/5/2014 11:19 AM, PotatoSauce wrote:
> On Saturday, July 5, 2014 2:00:03 PM UTC-4, Ross A. Finlayson wrote:
>> 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:
>>
>>>>
>>
>>>>
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>>>>
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>>>>
>>
>>>>
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>>>>>
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>>>>
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>>>>> If you are assuming from the start N doesn't exist
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>>>>
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>>>>
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>>>>
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>>>> I do not.
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>>>>
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>>>>
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>>>>
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>>>>> to prove that there is no bijection between N and Q, then your logic is entirely off.
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>>>>
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>>>>
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>>>>
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>>>> 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.
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>>>>
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>>>>>
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>>>>
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>>>>>
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>>>>
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>>>>>
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>>>>
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>>>>> You want lim card(s_n) to represent the cardinality of the sequence s_n "at infinity."
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>>>>
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>>>>
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>>>>
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>>>> I do not assume that a limit exists. But I show that the sets cannot get empty even if a limit exist.
>>
>>>>
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>>>
>>
>>> 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
>>
>>>
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>>> {} <= lim t->0 { t/2 } <= lim t-> 0 (-t,0) u (0, t) = {}
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>>>
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>>> (using <= for subset)
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>>>
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>>> So clearly, we can have non-empty sets with empty limit sets.
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>>>
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>>>
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>>>
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>>
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>> And so clearly the other way?
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>>
>>
>> You can see from topology
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>> running out either, I would hope.
>>
>>
>>
>> Would you agree that there are
>>
>> definitions in topology? At all?

>
> This is from a previous discussion. We have established that we are using the standard product topology on sets, and I was just reiterating parts that WM has previously agreed to.
>

As long as you'd agree:

1) that's a definition
2) there are others
3) there are usual "counterexamples in topology"
a) definition of open and closed
b) vacuity of
c) contradictions in empty closures from non-empty