Jump to content
Andrew26

Complexinfinity

Recommended Posts

What is infinity+i, infinity i+1 and infinity i+infinity?

i being the square root of -1 - the imaginary unit.

Share this post


Link to post
Share on other sites

Infinity is usually not thought of as a number; though there are some cases where you can think of it as a number, those cases treat infinity in different ways, meaning that to answer your question, I'd have to ask what you are trying to do with these "numbers".

Share this post


Link to post
Share on other sites
4 hours ago, uncool said:

 meaning that to answer your question, I'd have to ask what you are trying to do with these "numbers".

I second this. +1

5 hours ago, Andrew26 said:

What is infinity+i, infinity i+1 and infinity i+infinity?

i being the square root of -1 - the imaginary unit.

You might like to look at 'the point at infinity' in relation to complex numbers.

https://en.wikipedia.org/wiki/Riemann_sphere

Share this post


Link to post
Share on other sites

Given an open line segment, say (a, b), there are two ways to "compactify" it.  One, the "Stone-Cech compactification", is to add the "endpoints", a and b, to get [a, b].  Another, the "one point compactification" is to imagine bending the line segment into a circle and adding a single point at the join.  Following those ideas, we can "compactify" the set of all real numbers by adding "+ infinity" and "- infinity"  or by adding a single point, "infinity", so that the topology becomes that of a circle,

Similarly here are two different ways to "compactify" the open disk, [tex]\{(x, y)| x^2+ y^2< r^2\}[/tex].  The "Stone-Cech compactification", by adding the points on the boundary to get [tex]\{(x, y)| x^2+ y^2= r^2\}[/tex], and the "one point compactification" where you bend the disk up into a sphere, adding a single point at the top.  

We can do the same thing with the set of all complex numbers, adding an infinite number of "points at infinity", one in every direction, or add a single "point at infinity".  In the first case the topology is that of a closed disk and in the second the topology is that of a sphere.

Edited by Country Boy

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.