PlanetMath font sandbox

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.”

— Leopold Kronecker

“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.”

— Albert Einstein

“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 $\\hat{x}\\bar{y}$

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))))))

$a\ot|b$ or $a\mid b$

brocard’s CONJECTURE and subAnalytic set

#include <planetMath.h>

while flag == True {

value = oper1 % oper2;

counter++;

}

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

$\\gcd(25,50)$

Also,

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