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middle point (1/2) of line between every Sierpinski's triangle which repeat same pattern as fractal is moment zero of zeta function at s = 1 which exact at x = 1/2 line if bottom line of Pascal triangle from 0 to 1, size of each 0 get 1/2 smaller, 1 prime difference of Euler product correspond to ever shrinking at both triangle , trivial 0 (-2,-4,-6) are extension of nontrivial 0 by R.O.S.E can see pattern of 0 from random walk of nature number.
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Rule of chaos game of Sierpinski's gasket is choose a start point to corner triangle take 1/2^n of line, repeat same process continuously infinity time if that start point on any line of gasket will form Sierpinski's gasket another wise have not pattern at all, rule of collatz conjecture n/2 will bring any number shrinking to 1 by triangle shrink 1/3 every time by 1/2^n rule, since 3n+1 and n/2 rule get odd, even number only, smallest even number is 1 by shrinking triangle which start from any number will reach it by (m*2^n-1)/3(reciprocal of (3n+1)/2) rule start from 1 to infinity except choose 3n in every column.
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Does anyone know of an online tutor for a Sets Functions and Relations proof writing course? I have botched two attempts at this class and I very desperately need an online tutor that can help me out over the summer. These are the two books I have used, and will be using "The Tools of Mathematical Reasoning" again in the fall when I take the course again. I understand the sections where we go over logic and truth tables, I sort of understand proving sets. I typically start off strong in my proofs, but then somewhere in the proof I get twisted up in my logic and where I'm trying to go that I just make a sloppy mess out of my proofs. I am not looking for free tutoring (but won't turn it down), but I definitely need a lot of help with this course. Office hours with teachers only somewhat helped when I could get there, and there are absolutely no local tutors I can get help from, especially not now that the semester is over. There's nothing I want more than to make sense of this and finally ace this class! I'm too far in college debt to give up now. 
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5/21/17
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Hey guys,
I posted about generalization and counterexamples. Your comments are highly appreciated.

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From random walk (3n+1)/2 of collatz conjecture to it's reciprocal (m*2^n-1)/3 apply to chaos game of Sierpinski's gasket for 1/2^n of any line on triangle , each triangle as attractor , by mod(x,p) = 1/2 when p<x of R.O.S.E on average connect to mod(x,p)/p = x*(1/p) when p>x of random matrix get it's moment of zero on x = 1/2 line for s = 1 by (2n)!/(n!)^2, from random walk of nature number to order of chaos of prime number.
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Continuing our Mental Maths May theme, we look at why mental maths is important for children:

http://teejaymaths.com/importance-mental-maths-children/


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Explore the Mandelbrot Set.https://www.teoria.com/jra/benoit/
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Euler product of 1/(1-1/p) of zeta function approach infinity imply Euler product of (1-(1/p)) equal 0 = 1 - 1 = (1/2-1/6-1/10..+1/30..+1/3-1/15...) - 1, prime counting function p(x) for x = 2^n-2, 2^n-1, 2^n, 2^n+1 when n is infinity large, p(2^n-1) - p(2^n-2) equal to 1 by mod(x,p(c))/p(c), p(c) are all possible combination of all prime number(p), 2^n-2 is even number which is not a prime, increasing 1 imply 2^n-1 is mersenne prime at infinity, p(2^n) - p(2^n-1) equal to 1 minus 1/(1-1/2)minus 1 equal to 1-(2-1) which is 0, because mod(2^n,2^s)/2^s = 0, sequence of 1/2^s minus 1 is 1/2,1/4,1/8..., p(2^n+1) - p(2^n) again equal to (1-1)+1 = 1, prove 2^n+1 is a prime number, deduce p(2^n+1) - p(2^n-1) = 1, and 2^n+1 - 2^n-1 = 2 prove they are twin prime at infinity.
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