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Results: 169   Search Terms: "Equivalency Function"
Pages: 12 [ 1 2 3 4 5 6 7 8 9 10 ... 12 | Next ] Sort By:
 
1) Re: Proof that w in w
Posted: Feb 21, 2016 3:50 PM, by: ross.finlayson@gmail.com
(This is where then induction would find a rational between each pair of standard reals.) Then, the "natural/unit equivalency function" or "sweep" or "drawing the line" is well-ordering the unit line ...

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2) Re: Hidden assumption of the diagonal argument
Posted: Jan 25, 2016 11:42 PM, by: ross.finlayson@gmail.com
http://pengkuanonmaths.blogspot.com/2016/01/hidden-assumption-of-diagonal-argument.html > or Word https://www.academia.edu/20805963/Hidden_assumption_of_the_diagonal_argument "So, the diagonal argument fails." That's rather strong. (PengKuan's counterexample for countability ...

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3) Re: Foundations of mathematics, let's try it again
Posted: Dec 30, 2015 7:02 PM, by: Jim Burns
n->d, d->oo; n, d e N > > is constant monotone strictly increasing, > and that 0, 1 e ran(f), that "1-f" ranges > 1, ..., 0, and that via laws of arithmetic > and a symmetry argument, then that ran(f) ...

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4) Re: Cardinality of the set of binary-expressed real numbers
Posted: Dec 6, 2015 1:15 PM, by: ross.finlayson@gmail.com
> > the summands or use them naively in arithmetic and algebra > > without the definition of the "generating function" or the > > series definition, but the limit is no different than the sum. > > ...

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5) Re: Properties of numbers with a twist
Posted: Nov 27, 2015 4:15 AM, by: ross.finlayson@gmail.com
the proof because it uses the addition of dyadic rationals > (numbers of the form n/2^m, n,m in Z). "Numbers" are usually the "elements" of these "orders" or "orderings". Here you're discussing properties ...

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6) Re: Need help with proof of Cantor's diagonal argument
Posted: Nov 5, 2015 1:18 PM, by: ross.finlayson@gmail.com
not a bijection since two strings correspond > > to one number--a number having two binary expansions." > > > > https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument#Real_numbers > > > > Alternatively, ...

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7) Re: Foundations of mathematics, and David Petry
Posted: Oct 23, 2015 11:39 AM, by: ross.finlayson@gmail.com
On Friday, October 23, 2015 at 7:58:01 AM UTC-7, Port563 wrote: > "Robin Chapman" <R.J.Chapman@ex.ac.uk> wrote in message > news:n0bct9$jg7$1@dont-email.me... > > On ...

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8) Re: Nonmeasurable set PROVED nonsense.
Posted: Aug 9, 2015 10:32 AM, by: ross.finlayson@gmail.com
counterexample among functions otherwise of uncountability of the real numbers. And no, set theory is not "doomed", neither the day's alternative in homotopy type theory with "univalency" describing this ...

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9) Re: About potential and actual infinity in actual set theory.
Posted: May 30, 2015 11:08 PM, by: ross.finlayson@gmail.com
Virgil, I claim to show the counterexample for Cantor's first and second proofs of uncountability: nested intervals antidiagonal binary rule powerset result continued fractions building expansions ...

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10) Set Theory is Doomed
Posted: May 21, 2015 6:50 PM, by: ross.finlayson@gmail.com
equivalency function, are the same. This with the existence result of the regular fibration of "univalency" (unitarity) or the differential components of unit, bringing measure theory down from ...

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11) Re: Proof of Uncountability of |R and 2^|N for WM and others who are
confused about Cantor's diagonal.

Posted: May 8, 2015 8:40 PM, by: ross.finlayson@gmail.com
The number-theoretic uncountability results don't hold for sweep, the natural/unit equivalency function. Also it is shown constructively to be onto the image of its range. ...

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12) Re: Proof of Uncountability of |R and 2^|N for WM and others who are
confused about Cantor's diagonal.

Posted: Apr 29, 2015 9:03 PM, by: ross.finlayson@gmail.com
No, Virgil, it can't, for that is eventually only defined for the range of the equivalency function. This is a result of a very long- winded discussion, conveniently a mathematical result, thus im ...

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13) Re: Real Numbers - Bottom Up or Top Down
Posted: Apr 6, 2015 7:09 PM, by: ross.finlayson@gmail.com
There is a geometry of defined points and spaces, as there is a geometry, of defined points and lines. The Equivalency Function, or sweep, modelled by real functions, is a counterexample to eac ...

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14) Null Axiom Theory
Posted: Dec 19, 2014 9:08 PM, by: ross.finlayson@gmail.com
The Null Axiom Theory for mathematics is still having the usual standard results for mathematics and more, not offered by modern mathematics. Here an axiomless system of natural deduction, technical ...

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15) Re: LIM (X-->oo) 2^X = ???
Posted: Sep 2, 2014 8:58 AM, by: ross.finlayson@gmail.com
ZG, "concomitant"'s definition here is "from both each together". And, the line-drawing function there ...

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