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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

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 ross.finlayson@gmail.com Posts: 1,214 Registered: 2/15/09
Re: Discussion with WM - Frustration reaches boiling point (What
is not clear?)

Posted: Jul 5, 2014 11:16 PM

On 7/5/2014 11:50 AM, PotatoSauce wrote:
> On Saturday, July 5, 2014 2:32:03 PM UTC-4, Ross A. Finlayson wrote:
>

>>
>> As long as you'd agree:
>>
>>
>>
>> 1) that's a definition
>>
>> 2) there are others

>
> Of course. I was not suggesting otherwise.
>
> I do believe that certain definitions are more intuitive than others, but that's more of an opinion than actual mathematics.
>

>>
>> 3) there are usual "counterexamples in topology"
>>
>> a) definition of open and closed
>>
>> b) vacuity of
>>
>> c) contradictions in empty closures from non-empty

>

Thank you, then how can we reconcile
(as they are) definitions that are as
naturally (un-)justified? Point being
here that the definitions have to be re-
iterated in the proofs to ward off what
otherwise (in as concise terms) is of
counterexamples (via definitions) in
topology.

Then, this has courtesy properties of
the numbers, then directly of the points
more or less as they are of topology,
that these definitions are basically localized.

There are extra features of the numbers and
in topology with point sets and etc. These
are relevant extra features and of course
where inherent and as of the fabric: real
features of the objects here of the mathematics.

So, in the sense of equal representation, how
do you most strongly _build_ his case? For,
surely as above if its equivocal then it's
irrelevant to some unequivocal fact. Point
being that what you'd share as conscientious
would be unequivocal, and not subject to any
defaults but of all the definitions.

Also you'd as well find it as much or more
clear that there are at least readers here
who wouldn't need that as an aid, and that
it's the realm of development, not instruction.

It's a point to be careful that you don't
find yourself un-conscientious, of the value
of conscience (again, here of mathematics).