PlanetMath font sandbox

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

=

ψ

(

s

0

)

=

s

0

+

k

×

p

s

i

(

s

0

)

)

is a failure function since

ζ

(

Ψ

(

s

0

)

generates infinitely many failures. Here k belongs to

ℕ

.

Proof: There is no loss of generality in takining

k

=

1

. By Taylor’s

theorem

ζ

⁢

(

s

0

+

ζ

⁢

(

s

0

)

)

=

e

ζ

⁢

(

s

0

)

-

1

since, by asumption,

ζ

⁢

(

s

0

)

is not equal to

0

.

Poliñac’s formula is

∏

i

=

1

π

⁢

(

n

)

p

i

∑

j

=

1

log

p

i

⁡

n

⌊

n

p

i

j

⌋

,

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

1

+

1

+

1

+

1

+

1

+

…

, 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

÷

7

or preferably,

3

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.

𝔸

⁢

𝔹

⁢

ℂ

⁢

𝔻

⁢

𝔼

⁢

𝔽

⁢

𝔾

⁢

ℍ

⁢

𝕀

⁢

𝕁

⁢

𝕂

⁢

𝕃

⁢

𝕄

⁢

ℕ

⁢

𝕆

⁢

ℙ

⁢

ℚ

⁢

ℝ

⁢

𝕊

⁢

𝕋

⁢

𝕌

⁢

𝕍

⁢

𝕎

⁢

𝕏

⁢

𝕐

⁢

ℤ

(

1

+

i

)

⁢

(

1

-

i

)

or

(

1

+

𝕚

)

⁢

(

1

-

𝕚

)

Stanisław Haček on the

properties

of

x

^

⁢

y

¯

Stanisław Haček on the properties of

x

^

⁢

y

¯

Øystein Ore or Øystein Ore

3

*

4

,

f

*

g

,

f

∗

g

27

3

=

3

(defun

factorial

) (n)

(cond ((= n 0) 1)

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

a

|̸

b

or

a

∤

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,

∑

i

=

0

4

(

8

i

)

=

163

.

Title

PlanetMath font sandbox

Canonical

name

PlanetMathFontSandbox

Date of creation

2013-03-22 16:45:32

Last modified on

2013-03-22 16:45:32

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

28

Author

PrimeFan (13766)

Entry type

Data Structure

Classification

msc 00A99

Generated on Tue Feb 6 22:21:30 2018 by

LaTeXML