On Fri, 19 Jul 2013 23:02:04 +0200, Kevin Wampler <nob### [at] nowherenet>  
wrote:

> 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).
>
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)

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

-- 
-Nekar Xenos-

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