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Representing trigonometric functions in a form of rational functions
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Representing trigonometric functions in a form of rational functions
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Representing trigonometric functions in a form of rational functions
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asked  Representing trigonometric functions in a form of rational functions 
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Nonstandard numbers and exponential form of Zeta function
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Aug
31 
answered  What does the generating function $x/(1  e^{x})$ count? 
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31 
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Why do Bernoulli numbers arise everywhere?
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Aug
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answered  Why do Bernoulli numbers arise everywhere? 
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Nonstandard numbers and exponential form of Zeta function
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comment 
Nonstandard numbers and exponential form of Zeta function
@მამუკა ჯიბლაძე I think the quantities of noncountable sets also can be expressed with these nonstandard numbers. 
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comment 
Nonstandard numbers and exponential form of Zeta function
@მამუკა ჯიბლაძე it would be great if I could express zeta purely in elementary functions. Or express exponentiation through zetas. For me it was also a surprize that the two kinds of Bernoulli numbers correspond to the powers of two infinities. And the usually used infinity, the quantity of natural numbers is not purely nonstandard contrary to what is usually assumed in surreals and ordinal arithmetic. 
Aug
30 
comment 
Nonstandard numbers and exponential form of Zeta function
@Noah Schweber $\tau$ lies in between $\omega_$ and $\omega_+$ which are both not purely nonstandard. I think symbol $\tau$ thus can be useful: $\tau+1/2=\omega_+$ (the quantity of nonnegative integers), $\tau1/2=\omega_$ (the quantity of natural numbers). $\tau$ is the quantity of all even numbers, it is the quantity of all odd numbers and taken twice it is the quantity of all integers. 
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Nonstandard numbers and exponential form of Zeta function
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Nonstandard numbers and exponential form of Zeta function
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Nonstandard numbers and exponential form of Zeta function
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Nonstandard numbers and exponential form of Zeta function
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Nonstandard numbers and exponential form of Zeta function
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Nonstandard numbers and exponential form of Zeta function
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Nonstandard numbers and exponential form of Zeta function
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Nonstandard numbers and exponential form of Zeta function
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