# Questions tagged [numerical-systems]

This tag is intended for extensions of real numbers, such as hypercomplex numbers, surreal numbers, non-standard analysis, games etc.

3
questions

3
votes

3
answers

454
views

### Did anyone ever introduce an "oscillating unity"?

I wonder whether anyone ever tried to introduce an extension of real numbers by adding an element $\nu$ which would signify the behavior of the function $(-1)^x$ as $x$ goes to infinity?
In other ...

0
votes

0
answers

125
views

### Is standard, affine infinity of extended reals quite small on the scale of infinities?

Some time ago I had a conversation with a guy who was into surreal numbers and he said that in surreal numbers the affine infinity is quite minor entity compared to the ordinality of natural numbers $\...

1
vote

1
answer

410
views

### What are the consequences if we could express tangent via logarithm in an algebraic system? [closed]

Working on an algebra of divergent integrals I came to the following relation:
If $\tau=\int_0^\infty dx$ then
$$\ln (\tau+a)=\int_{0}^\infty \psi'(x+1/2+a)dx$$
and this directly gives the following ...