
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 UTC4, 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 nonempty >
Thank you, then how can we reconcile those definitions with other adhoc (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 unconscientious, of the value of conscience (again, here of mathematics).

