> Yes, we know (by the Continuum Hypothesis, Cantor) that > betweeness is infinite--not just "huge." Suppose > we reject the CH? Every sequence is then finite > and differs from another sequence that infinitely > approaches, but does not reach it, by an infinitesimal > margin. (This is the insight, of course, that led > to the development of analysis--the study of continuous > functions.)
Sorry, but I have no idea what you are trying to express here. How is the Continuum Hypothesis relevant here?
-- "But remember, as long as one human being follows the rules of mathematics, then mathematics as a human discipline survives. Right now I'm that one human being, so mathematics survives." -- James S. Harris