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Let the definition of a failure, in the context of Riemann Hypothesis, be a non-root. Let $s_{0}$ be a non-root. Then $s=\psi(s_{0})=s_{0}+k\times\\ psi(s_{0}))$ is a failure function since $\zeta(\Psi(s_{0})$ generates infinitely many failures. Here k belongs to $\mathbb{N}.$

Proof: There is no loss of generality in takining $k=1$. By Taylor’s theorem $\zeta(s_{0}+\zeta(s_{0}))=e^{{\zeta(s_{0})}}-1$ since, by asumption, $\zeta(s_{0})$ is not equal to $0$.

Poliñac’s formula is

$\prod_{{i=1}}^{{\pi(n)}}{p_{i}}^{{\displaystyle\sum_{{j=1}}^{{\log_{{p_{i}}}n}% }\lfloor\frac{n}{{p_{i}}^{j}}\rfloor}},$ |

Ich ziemlich muß hab eine Wiener Strüdel!

“God made the integers, and all the rest is the work of man.”

“A mathematician is a device for turning coffee into theorems.”

— Pal Erdős

“Mathematics possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture.”

— Bertrand Russell

“Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.”

— Bertrand Russell

“As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.”

“I had a feeling once about Mathematics, that I saw it all — Depth beyond depth was revealed to me — the Byss and Abyss. I saw, as one might see the transit of Venus or even the Lord Mayor’s Show, a quantity passing through infinity and changing its sign from plus to minus. I saw exactly why it happened and why the tergiversation was inevitable: and how the one step involved all the others. It was like politics. But it was after dinner and I let it go!”

— Winston Churchill

“Math, my dear boy, is nothing more than the lesbian sister of biology.”

— Peter Griffin, Family Guy, “When You Wish Upon A Weinstein”

“How about we fire up the old Segway and find a nice quiet field to do long division in? I mean, a nice quiet field in which to do long division. Sorry, sorry, everybody.”

— Neil Goldman, Family Guy, “8 Simple Rules for Buying My Teenage Daughter”

Consider $\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\ldots}}}}}$, etc., in TeX as `$\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\ldots}}}}}$`

.

In TeX and LaTeX we may write $3^{{4/7}}$ or $3^{{4\div 7}}$ or preferably, $3^{{\frac{4}{7}}}$.

Stanley Skewes in 1933 gave the lower bound $e^{{e^{{e^{{79}}}}}}$, approximately $10^{{{10}^{{{10}^{{34}}}}}}$.

Wolfgang Berg moved to the States in 1934, and Wacław Sierpiński followed in 1938.

$\mathbb{A}\mathbb{B}\mathbb{C}\mathbb{D}\mathbb{E}\mathbb{F}\mathbb{G}\mathbb{% H}\mathbb{I}\mathbb{J}\mathbb{K}\mathbb{L}\mathbb{M}\mathbb{N}\mathbb{O}% \mathbb{P}\mathbb{Q}\mathbb{R}\mathbb{S}\mathbb{T}\mathbb{U}\mathbb{V}\mathbb{% W}\mathbb{X}\mathbb{Y}\mathbb{Z}$

$(1+i)(1-i)$ or $(1+\mathbb{i})(1-\mathbb{i})$

Stanisław Haček on the properties of $\hat{x}\bar{y}$

Stanisław Haček on the properties of $\hat{x}\bar{y}$

Øystein Ore or Øystein Ore

$3*4$, $f*g$, $f\ast g$

$\sqrt[3]{27}=3$

(defun factorial) (n)

(cond ((= n 0) 1)

(t (* n (factorial (- n 1))))))

$a\not|b$ or $a\nmid b$

brocard’s CONJECTURE and subAnalytic set

#include <planetMath.h>

while flag == True {

value = oper1 % oper2;

counter++;

}

while flag == True { value = oper1 % oper2; counter++; }

$\gcd(25,50)$

or

Also,

$\sum_{{i=0}}^{4}{8\choose i}=163.$ |

## Mathematics Subject Classification

00A99*no label found*

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