On 7/19/2013 2:38 PM, Nekar Xenos wrote:
> I imagined the complex set would have a larger "density" if you could
> call it that. (Real numbers would have a larger "density" than integers)

What you mean be "density" is a whole 'nother issue which is 
surprisingly complex when you get into it.  When talking about questions 
like "Infinity+Infinity" it's best not to worry about things like "density".

 > So if I have this right
 > Infinity + Infinity =  Infinity
 > is correct for real numbers and not for complex numbers.

That's basically correct.  More precisely, for the definition of 
infinity which turns out to be most useful for the reals 
Infinity+Infinity=Infinity.  For the definition of Infinity which turns 
out to be the most useful for the complex numbers Infinity+Infinity is 
undefined.

People can (and occasionally do) use different definitions of Infinity 
for the reals/complexes than these, depending on what's useful for the 
problem they want to solve.  But you've got the right idea for the most 
common choices.

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