Re: Proof 0.999... is not equal to one.

"T.H. Ray" <thray123@xxxxxxx> writes:

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
.

Relevant Pages

  • Re: Review of Mueckenheims book.
    ... as 'sequence' itself has a mathematical definition. ... explain what "infinite numbers" are. ... classical mathematics, including mathematical logic, ZFC, and is non- ...
    (sci.math)
  • Re: Panu Raatikainens review of two of Chaitins books.
    ... "AIT will lead to the major breakthrough of 21st century mathematics, ... which will be information-theoretic and complexity based characterizations ... because they don't discern a distinctive pattern or closest fitting analogy ... "Consider the problem of finding a rule for generating a sequence ...
    (comp.theory)
  • Re: What is md5sum?
    ... Mathematics is not an approximation of anything. ... > of the sitauation in the real universe? ... you need *at least* the number of digits of the sequence to do that. ... > the same md5sum, you find yourself curiously unable to CHOOSE a pair to ...
    (comp.os.linux.setup)
  • Re: Sets question (maybe)
    ... In mathematics, it's usually referred to as a finite sequence (or just ... function/ which takes the naturals (often just written as ... numbers a, b, you want to be able to talk about the ordered pair (j_a, ...
    (sci.math)
  • Re: Cantor Confusion
    ... But that does not change the sequence at all, ... We know that the sum cannot be larger than 2. ... to find the last node of an infinite path, i.e. the node that contributes 1 ... In that case you should throw away *all* of mathematics, ...
    (sci.math)