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- 09-07-2016, 03:03 PM #11

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- 09-07-2016, 03:11 PM #12--Inter Arma Enim Silent Leges--

“Science needs the light of free expression to flourish. It depends on the fearless questioning of authority, and the open exchange of ideas.” ― Neil deGrasse Tyson

"When photons interact with electrons, they are interacting with the charge around a "bare" mass, and thus the interaction is electromagnetic, hence light. This light slows the photon down." - BuleriaChk

- 09-07-2016, 03:32 PM #13

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- 09-07-2016, 06:29 PM #14

- 09-07-2016, 06:36 PM #15
## Re: The Golden Ratio Award Nominations 2016

--Inter Arma Enim Silent Leges--

“Science needs the light of free expression to flourish. It depends on the fearless questioning of authority, and the open exchange of ideas.” ― Neil deGrasse Tyson

"When photons interact with electrons, they are interacting with the charge around a "bare" mass, and thus the interaction is electromagnetic, hence light. This light slows the photon down." - BuleriaChk

- 09-07-2016, 10:14 PM #16

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- 09-07-2016, 11:27 PM #17

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## Re: The Golden Ratio Award Nominations 2016

sources:

http://www.math.wustl.edu/~kumar/cou...2009/peano.pdf

https://en.wikipedia.org/wiki/Homomorphism

https://en.wikipedia.org/wiki/Dedekind-infinite_set

https://en.wikipedia.org/wiki/Transfinite_number

https://en.wikipedia.org/wiki/Contin...uum_hypothesis

https://en.wikipedia.org/wiki/Uncountable_set

https://en.wikipedia.org/wiki/Set_th...tic_set_theory

https://en.wikipedia.org/wiki/Injective_function

https://en.wikipedia.org/wiki/Axiom_of_choiceLast edited by 7777777; 09-08-2016 at 02:46 PM.

- 09-08-2016, 07:42 AM #18
## Re: The Golden Ratio Award Nominations 2016

I'm not sure where all this comes from, but the last part of the second-to-last paragraph appears to be directly lifted (and out of context) from this paper (Section 5, page 17):

https://www.scribd.com/doc/317032966...-de-numere-pdf

Let Z be the set of equivalence classes under this relation. But, now, alas we have lost any semblance of the minimal element property which was so important and desirable. In other words, there are now subsets of Q which are bounded below with no minimal element in sight. (Not just in the set, but not even in Q).*Construction of Number Systems*, by N. Mohan Kumar, is posted to a few other Scribd sites, some of which are behind pay walls.

- 09-08-2016, 08:26 AM #19

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## Re: The Golden Ratio Award Nominations 2016

Look here

- 09-08-2016, 09:15 AM #20
## Re: The Golden Ratio Award Nominations 2016

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