In 2/14/2013 9:38 AM, Shmuel (Seymour J.) Metz wrote: > In <Y66dnSxkWL2pJITMnZ2dnUVZ_r2dnZ2d@giganews.com>, on 02/11/2013 > at 09:38 PM, fom <fomJUNK@nyms.net> said: > >> You may be unaware that identity in set theory >> is not the same as what you have described with >> your explanation above. > > He wrote "indistiguishable", which is a differnet notion. >
The full text of the original post was about identity.
It was about a particular form of stipulative identity that arises when considering the definition of the real numbers in terms of Dedekind cuts.
At the end of the post, the mechanism used to do the analysis was re-interpreted so that its topological aspects could be considered.
Certainly, you are correct that there are various contexts. But, one aspect of foundational investigations is to sort out the logical priority of structures.
I am fully aware of much that is written in topology texts. The last part of that post points out that any countable language with a sign of negation and interpretation with respect to bivalent logic may possibly be represented with a minimal Hausdorff topology.
So, is topology foundational?
Can't seem to get a discussion on *hard* questions.
Thank you for your observation, however. I shall try to be more careful when explaining myself in the future.