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Results: 168   Search Terms: "Equivalency Function"
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1) Re: A number is the measure of a magnitude. There is no other way to
derive numbers.

Posted: Jan 20, 2017 10:12 PM, by: ross.finlayson@gmail.com
accommodate the usual conveniences of the utility of the general representations of numbers, up to the "unique up to isomorphism" complete ordered field, (besides any putative definitions of field operations ...

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2) Re: Dan says infinite is well defined but can never tell whether a
number is finite or infinite Re: Cantor's Diagonal Argument -- a formal proof

Posted: Jan 6, 2017 1:02 PM, by: ross.finlayson@gmail.com
what's EF? No, EF is: f_d(n) = n/d, d -> oo, n -> d, n, d e N. Then, ran(EF) is [0,1]. EF is the "Equivalency Function". Your absurd fru-fru pooh-pooh is not withstanding. Cantor proves the line is ...

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3) Re: Cantor's Diagonal Argument -- a formal proof
Posted: Jan 4, 2017 2:36 PM, by: ross.finlayson@gmail.com
In the preface to his published proof (http://www.logicmuseum.com/cantor/diagarg.htm), Cantor said "However, there is a proof of this proposition that is much simpler, and which does not depend on considering ...

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4) Re: Be careful with the infinite, dont mix up lists and trees
Posted: Jan 3, 2017 2:18 AM, by: ross.finlayson@gmail.com
> > > Some mathematical invention by Ross A. Finlayson > > that is essentially secret? > > Canon "Electro-Focus"? Empty/Full? It's the natural/unit equivalency function, with the domain being the ...

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5) Re: Be careful with the infinite, dont mix up lists and trees
Posted: Jan 3, 2017 1:45 AM, by: ross.finlayson@gmail.com
On Monday, January 2, 2017 at 10:21:06 PM UTC-8, burs...@gmail.com wrote: > > You say "it doesn't make sense", > > No I didn't say that. I only said it > doesn't make sense to use trees ...

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6) Re: WM's alleged counting of |R
Posted: Dec 10, 2016 11:12 PM, by: ross.finlayson@gmail.com
another of WM's many lies about mathematics is again revealed as > the lie it is. > -- > Virgil > "Mit der Dummheit kampfen Gotter selbst vergebens." (Schiller) There's only one bijection between N ...

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7) Re: Lists of binary sequences and uncountability
Posted: Nov 26, 2016 6:26 AM, by: PengKuan Em
Le samedi 26 novembre 2016 04:03:36 UTC+1, Ross A. Finlayson a écrit : > The Equivalency Function, or sweep(), has > a range that is a continuous domain, and > otherwise is unique as the counterexam ...

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8) Re: Cantor's FIRST proof of uncountability
Posted: Oct 5, 2016 12:12 AM, by: ross.finlayson@gmail.com
So neither WM nor JG have any justifiable way to claim the reals are > countable. > -- > Virgil > "Mit der Dummheit kampfen Gotter selbst vergebens." (Schiller) Why don't you write out each of the three ...

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9) Re: Ping FredJeffries
Posted: Sep 3, 2016 5:09 PM, by: ross.finlayson@gmail.com
Wilde, Lady Windermere's Fan I'd ask you first to write the definition and properties of sweep, the "equivalency function", which is n/d, n -> d, d -> oo, for n, d e N, that its range is of the image ...

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10) 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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11) 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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12) 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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13) 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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14) 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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15) 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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