On 7/19/2013 1:48 PM, Nekar Xenos wrote:
>
> I think I could say the specific infinity I'm thinking of would be the
> biggest type of infinity.
> What would that be?
> Complex Infinity? (if that could be considered)
>

There are two different ways I'm tempted to interpret your question, but 
only one of them makes sense.  I'll try to answer them both anyway:

Q1) "Out of all the different ways you can define Infinity, what's the 
biggest?

A1) Because the different definitions of Infinity use different 
definitions of what a "number" is, there is no way to compare them at 
all to say which is bigger -- they are just completely different things. 
  It's like asking "which is bigger, 4 or fish?".

Q2) "You mentioned that for some definitions you get multiple different 
types of infinity, what's the biggest of those?"

A2) The answers depends on what particular definition of Infinity you're 
talking about, but the most common answers is that there is no biggest 
Infinity -- just like there's no biggest finite integer.  Sometimes 
people will try to add a "biggest infinity" to things, but you don't 
generally allow addition with it anyway.

---

As I mentioned in (A1), it doesn't make sense to ask if "complex 
Infinity" is bigger than another definition of infinity.

As an aside, a notion of "complex Infinity" is actually extremely useful 
in some areas mathematics.  Arguably much more useful than "real 
Infinity" is.  The standard definition of complex Infinity does not 
allow Infinity+Infinity though (it treats it as undefined, much like 1/0 
is commonly treated as undefined for the reals).

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