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Natural Deductions

Expository preaching, non-rigorous proofs

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Natural Deductions | natural-deductions.blogspot.com Reviews
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Expository preaching, non-rigorous proofs
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1 natural deductions
2 pythagorean triples
3 number theory notes
4 posted by
5 muad`dib
6 no comments
7 labels pythagorean triple
8 cauchy product
9 end{tabular}
10 labels cauchy
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natural deductions,pythagorean triples,number theory notes,posted by,muad`dib,no comments,labels pythagorean triple,cauchy product,end{tabular},labels cauchy,convergence,infinity,mertens,series,in this,frac{ pi}{2} $,4}{ infty,frac{ infty,labels infinity
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Natural Deductions | natural-deductions.blogspot.com Reviews

https://natural-deductions.blogspot.com

Expository preaching, non-rigorous proofs

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1

Natural Deductions: Infinity factorial and Wallis' formula

http://natural-deductions.blogspot.com/2010/04/infinity-factorial-and-wallis-formula.html

Expository preaching, non-rigorous proofs. Thursday, 22 April 2010. Infinity factorial and Wallis' formula. In his second letter to Hardy, Ramanujan stated:. 1 2 3 4 cdots = - frac{1}{12}$. Hardy could tell Ramanujan was a genius from this equation because he must have developed the theory of the zeta function, and its functional equation. Excellent note by Dror Bar-Natan, we start with the following equations:. 1 times 2 times 3 times 4 times cdots = sqrt{2 pi}$ $ 1 1 1 1 cdots = - frac{1}{2}$.

2

Natural Deductions: Euler Zeta Function

http://natural-deductions.blogspot.com/2010/04/reimann-zeta-function.html

Expository preaching, non-rigorous proofs. Thursday, 22 April 2010. Definition: $ zeta(s) = 1 frac{1}{2 s} frac{1}{3 s} frac{1}{4 s} cdots $ (1). Theorem: $ zeta(s) = frac{1}{1 - frac{1}{2 s} times frac{1}{1 - frac{1}{3 s} times frac{1}{1 - frac{1}{5 s} times frac{1}{1 - frac{1}{7 s} times cdots$ (2). Dirichlet's theorem states on the arithmetic progression (for $(a,k) = 1$) $ a, a k, a 2k, a 3k, cdots $ there are infinitely many primes. Let us recalibrate our weapon so it can operate on these arithm...

3

Natural Deductions: Cauchy Product

http://natural-deductions.blogspot.com/2010/04/we-have-two-convergent-sequences-sumn1.html

Expository preaching, non-rigorous proofs. Thursday, 22 April 2010. We have two convergent series,. A n = sum n {k=0} a k $ and $ B n = sum n {k=0} b k $. Theorem: Cauchy Product $ C infty = A infty B infty = sum {k=0} sum {i=0.k} a i b {k-i} $. Demonstration: The product is the sum of the sums anti-diagonals of this table:. Begin{tabular}{ c c c c c }. A 0 b 0) and (a 1 b 0) and (a 2 b 0) and (a 3 b 0) and a 4 b 0 and hline. A 0 b 1) and (a 1 b 1) and (a 2 b 1) and a 3 b 1 and a 4 b 1 and hline.

4

Natural Deductions: This is not a test!

http://natural-deductions.blogspot.com/2010/04/this-is-not-test.html

Expository preaching, non-rigorous proofs. Thursday, 22 April 2010. This is not a test! Sqrt[5]{1} = - frac{1}{4} quad frac{1}{4} cdot sqrt{5} quad frac{1}{2} cdot sqrt{- frac{5}{2}- frac{1}{2} cdot sqrt{5}. Ripped out of Constructing Regular Polygons - Primitive Roots of Unity. Subscribe to: Post Comments (Atom). LaTeX equations are rendered using MathML).

5

Natural Deductions: A radical expression for 1

http://natural-deductions.blogspot.com/2010/05/radical-expression-for-1_22.html

Expository preaching, non-rigorous proofs. Saturday, 22 May 2010. A radical expression for 1. Sqrt{3}{ sqrt{5} 2} - sqrt[3]{ sqrt{5}-2} $. Subscribe to: Post Comments (Atom). LaTeX equations are rendered using MathML).

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Natural Deductions

Expository preaching, non-rigorous proofs. Saturday, 5 June 2010. C 2 = a 2 b 2 $ factors as $ (a ib)(a-ib) $ so let $ a ib = (p iq) 2 = p 2-q 2 i(2pq) $ and $ a-ib = (p-iq) 2 = p 2-q 2 - i(2pq) $ now $ c = (p iq)(p-iq) = p 2 q 2 $. In conclusion, if we pick $ p $, $ q$ then ($ p 2 - q 2 $, $ 2pq $, $ p 2 q 2 $) forms a pythagorean triple. Saturday, 22 May 2010. A radical expression for 1. Sqrt{3}{ sqrt{5} 2} - sqrt[3]{ sqrt{5}-2} $. Thursday, 22 April 2010. We have two convergent series,. Hardy could te...

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