On Dec 31, 1:18 pm, Virgil <vir...@ligriv.com> wrote: > In article > <6eaa4cc3-ff1d-4cf0-b271-00155cca9...@oi3g2000pbb.googlegroups.com>, > "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote: > > > > > > > > > > > On Dec 30, 9:58 pm, Virgil <vir...@ligriv.com> wrote: > > > In article > > > <166aaacd-16b6-47b8-925b-bb5b42023...@vb8g2000pbb.googlegroups.com>, > > > "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote: > > > > > This is from that, the constructed sequences (here ordinally-valued) > > > > of nesting endpoints, of an interval, either meet or don't. > > > > In comprehensible! > > > > Why is it that Ross' attempts at expression himself about things > > > mathematical are always more obfuscating than clarifying? > > > > The rest is silence! > > > -- > > >http://en.wikipedia.org/wiki/The_Oak_and_the_Reed > > But Ross is, as yet, no more than an acorn. > --
Ah, that's rich. It's a rather poor metaphor, but how low you'll stoop for it is notable.
Unless you've discovered some way to blank the memory of others, there are quite a few who could recount the salient points from memory, at least of the definition of what the E.F. or EF is, whether or not they would care to defend it or discount it. And, even though you've displayed of yourself a lack of memory, I wouldn't so ascribe that lack thereof to others.
So, in the well-ordering of the reals, for any initial segment, as defined by an ordinal, where the well-ordering is a function from the ordinals onto the reals, in the course-of-passage there is a concomitant interval defined by the elements of the reals in their well-order. These intervals, nested in the previous, see that the endpoints converge. Do they meet? If they don't, the interval is non- empty, and there's not an element of the reals there, eventually in order. If they do meet, where there are no points within the interval, they are consecutive, or duplicate.
You could well note that the interval endpoints converge to each other, in the countably infinite. The endpoints meet: or don't. Cantor's first has their intersection: non-empty.