The number circle revisited

[Keiji]

http://en.wikipedia.org/wiki/User:INVER ... ber_Circle

That's all my relevant findings...

[Nick]

If you go forwards OR backwards from 0, you will reach infinity. This doesn't make much sense for me. However, saying that there is such a thing as negative infinity doesn't make much sense either. I suggest making one point 0 and the other the absolute value of infinity. What do you think?[/b]

[Keiji]

If you go forwards OR backwards from 0, you will reach infinity. This doesn't make much sense for me. However, saying that there is such a thing as negative infinity doesn't make much sense either. I suggest making one point 0 and the other the absolute value of infinity. What do you think?[/b]

Simple proof that positive and negative infinity are the same:

We know k*infinity = infinity where k != 0
Let k = -1
Therefore -infinity = infinity

Anyway, the vertical position is related to the absolute value of the number, and the sign is which side you're on. This is a specific case of the more general number sphere, where the vertical position is related to the absolute value of the number, and the angle/argument is the horizontal angle taken from the center. Since infinity and zero both lie in the same vertical line as the center of the sphere (or circle), it makes no sense to give infinity an angle/argument and therefore no sense to give it a sign.