Start of the Thread " Infinities "

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Quote:
Originally Posted by R.D. Silverman View Post
Whether such a discussion would be useful depends on several things.

(1) Whether it is well grounded in its use of definitions and axioms.
(2) Whether participants are just going to resort to hand waving and/or
attempts to use vague colloquial English to describe mathematics.
(3) Whether participants have enough background knowledge to be able to
say anything intelligent.

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I agree with RD S, and his three points, and that is a good basis in which to start. I am trying to do that in what I have been putting together since yesterday. I would like very much to be facile with mathematical techniques, and realize wonderous notation, and whenever I can I will. I notice that TeX is available so I will rely on that to make things appear clean.

If Weierstrass, Dedekind, Cantor and Godel have already touched on some of my thoughts, (and they probably have ) I apologize in advance if I restate what they may have mentioned. I want to see how I would gather my thoughts, and then present them.

I will be using Hawking's " God Created the Integers " as my basic resource but may wander towards Penrose's " The Road to Reality " to relate more modern thinking. I will also want to philosophize mathematically, if only to help steer my thinking to the next mathematical step of where I am going.

I think that I do not have an agenda, except to make sure that there are no murky areas in my thoughts.

So what advice do folks and members want to give on what I have stated so far ?

Simon

PS Some of this will include questions that I want to pose, and some assertions, which will hopefully be based on what has preceded these.

PPS I will start my thread in the " Miscellaneous Mathematics " as a starting point.

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Here are some of my textbooks:

A Course in Pure Mathematics 1908
G H Hardy

An Introduction to the Theory of Numbers (6th) 2008
G H Hardy
E M Wright

Elementary Number Theory ( 6th ) 2007
David M Burton

An Introduction to Analytic Number Theory 1976
Tom M Apostol

Algebraic Number Theory ( 2nd ) 1994
Serge Lang

Classical Introduction to Modern Number Theory ( 2nd ) 1990
Kenneth Ireland
Michael Rosen

Elementary Number Theory 1998
Gareth A Jones
J Mary Jones

An Introduction to Mathematical Cryptography 2008
Jeffrey Hoffstein
Jill Pipher
Joseph H Silverman

The Art of Computer Programming ( 4 volume set ) 2010
Donald E Knuth

plus even more that may be mentioned later .

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By the way, if any of you visit D E Knuth's website will notice that he and his wife have traveled extensively and taken countless ( not really countless ) pictures of curiously strange highway signs. Merritt BC is mentioned to have a sign close to the hospital; it is truly there .