Venkat!

Venkat,

Can you really hope to refute all this?:

Construction of natural numbers and definition of equality without
measures or
"size" or even arithmetic:
http://www.ms.uky.edu/~lee/ma502/notes2/node7.html

(Take a read of that last sentence: "Notice that there is no mention
of such things
as addition or multiplication.")

Construction of the continuum without reference to lengths, points,
whatever:
http://en.wikipedia.org/wiki/Construction_of_real_numbers

Definition of "continuum" as it relates to mathematics and NOT
physics:
http://mathworld.wolfram.com/Continuum.html

The axioms of the Zermelo-Fraenkel set theory:
http://www.ltn.lv/~podnieks/gt2.html

Different sizes of infinity:
http://mathworld.wolfram.com/CardinalNumber.html
http://mathworld.wolfram.com/OrdinalNumber.html
Theorem: http://planetmath.org/encyclopedia/CantorsTheorem.html
Proof: http://planetmath.org/encyclopedia/ProofOfCantorsTheorem.html

Measure Theory:
http://wwwmaths.anu.edu.au/~john/Assets/Lecture%20Notes/measure_theory.pdf

Infinitesimals, Infinity, and the Surreal Numbers:
http://en.wikipedia.org/wiki/Surreal_number

Non-standard Analysis:
http://www.sun-inet.or.jp/~leibniz/math/nsa.html
.

Relevant Pages

  • Re: real valued modulo math
    ... valued continuum has not been performed on that page. ... In that the ring created is a new ring then ... I have no doubt that the construction which I speak of is a valid math ... Clearly a modulo format is what I am making try to fit the quotient ...
    (sci.math)
  • Re: The Law of the Excluded Middle again (long)
    ... The Continuum is exposition, ... response, you gave a reference. ... concepts of system and process precede the construction. ... In saying that, I am not saying I have nothing to learn. ...
    (sci.math)
  • Re: Cantors diagonal proof wrong?
    ... > its construction ensures there is no repetition anywhere after the ... What is the first digit? ... > stage I grasped 'infinity' as a serious of steps, ... But in a line enumerated by omega, also Cantor could not ...
    (sci.math)
  • Re: The Law of the Excluded Middle again (long)
    ... The Continuum is exposition, ... use the Wikipedia reference: ... I was trying to get you to appreciate Weyl's construction ... generating processes just as they do in contemporary ...
    (sci.math)
  • Re: The Law of the Excluded Middle again (long)
    ... The Continuum is exposition, ... response, you gave a reference. ... construction. ... In saying that, I am not saying I have nothing to ...
    (sci.math)
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