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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On 19/07/2013 11:31 PM, Nekar Xenos wrote:

>
> High school maths...
>

Like me then. What everyone is saying is correct but they are saying it 
with the understanding of the language "mathematics". It is not what we 
mortals understand as the same language that we speak. There is no 
option but to learn it or consign it to "all very well but does it pay 
the bills". (A topic I will leave to the tabloids. :-) )

I've read a little about it and to be truthful if the threat goes any 
deeper then it goes over my head. Infinity is a great thought but after 
a while. My eyes cross when I try focusing on it.

-- 
Regards
     Stephen

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>>> 2) What is addition?
>>>
>>> And in addition, for your question:
>>
>> I SEE WHAT YOU DID THERE! ;-)
>
> +1

"Add one"?

I SEE WHAT YOU DID THERE! :-D

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On 19/07/2013 11:38 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)
>

Why don’t I mix it a little. :-D

Imagine infinity * infinity.
Which is infinity ^2

Now think about infinity ^ infinity.

Night night. ;-)

(Sorry I'm in that sort of mood. I've had a long day.)

-- 
Regards
     Stephen

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On 19/07/2013 11:46 PM, Orchid Win7 v1 wrote:
>>>> 2) What is addition?
>>>>
>>>> And in addition, for your question:
>>>
>>> I SEE WHAT YOU DID THERE! ;-)
>>
>> +1
>
> "Add one"?
>
> I SEE WHAT YOU DID THERE! :-D

And I saw what YOU did there.

Unfortunately I wrote plus one.
Which is different to plus four's

-- 
Regards
     Stephen

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On Fri, 19 Jul 2013 23:49:26 +0200, Stephen <mca### [at] aolcom> wrote:

> On 19/07/2013 11:38 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 intege
rs)
>>
>
> Why don’t I mix it a little. :-D
>
> Imagine infinity * infinity.
> Which is infinity ^2
>
> Now think about infinity ^ infinity.
>
> Night night. ;-)
>
> (Sorry I'm in that sort of mood. I've had a long day.)
>

How about:

Complex Infinity ^ Complex Infinity

But I suppose if you can't add them, you can't power them...

-- 

-Nekar Xenos-

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On 7/19/2013 2:32 PM, Stephen wrote:
>
> Damn! that was what I was going to do but thought that it was too big a
> leap to say that infinity * infinity = infinity. From what I had written
> before.
> So out of (a passing) interest what is the difference?
>
> PS the passing is my little joke. ;-)
>

I'm trying to think of an answer which won't make you regret asking that 
question :)

For some definitions of infinity there isn't a difference and 2*infinity 
= infinity*2 = infinity

The most common definition of infinity for which there *is* a difference 
can be thought of as reasoning about (possibly infinitely long) 
sequences of things.  In order to not get into the confusing details 
about this, let me just say that it turns out that if you follow this 
logic through you find that you're allowed to take a sequence, A, and 
create a new sequence by replacing each entry in A with another sequence B.

Let me give an example.  I'll denote each element in a sequence tieh the 
character @.  You can represent a finite number by a sequence of a 
certain length, so 1 is "@", 2 is "@@", 3 is "@@@", 7 is "@@@@@@@" etc. 
  So let's say we take the sequence for 3:

@@@

and replace each element in it by the sequence for 2, the we get:

(@@)(@@)(@@)

Where I've put parentheses in for readability.  Writing it without the 
parens you get:

@@@@@@

Which is the sequence of 6.  And what a coincidence 2*3 = 6!  In fact, 
this strange process works exactly like the multiplication you've come 
to know and love for all finite numbers.  Since it works just like 
multiplication, we'll just say that this is what we mean by multiplying 
two of these sequences together (if it walks like a duck and it quacks 
like a duck).  Here's a slightly more precise definition:

If A and B are sequences, then by "A*B" we mean the sequence which would 
result by replacing each element in B by the sequence A.

By this definition:

2*3 = (@@)*(@@@) = (@@)(@@)(@@) = @@@@@@ = 6
3*2 = (@@@)*(@@) = (@@@)(@@@) = @@@@@@ = 6

So we get 2*3 = 3*2 = 6 like you'd expect.  But notice that the 
parentheses were different in that middle step.  This is where 
everything goes to hell when you allow infinite sequences.

Let me give an example.  Say you've got your basic infinite sequence 
(which I'll write as "w" since writing "infinity" get confusing when you 
have more than one infinity).  So:

w = @@@@@...

Where the "..." just means "goes on forever".  I won't force you to 
endure a mathematically precise definition of that.  So with our 
previous definition of multiplication:

2*w = (@@)(@@)(@@)... = @@@@@@... = w
w*2 = (@@@@...)(@@@@...) = @@@@...@@@@... = now you may be confused

I don't have a way to make that w*2 feel like it's not a little crazy, 
but the best I can do is restate it in plain English:

2*w = "count in forever in multiple of two"
w*2 = "count forever, then when you're done, do it again."

So while counting forever by multiples of two is basically the same as 
counting forever normally, counting forever and then doing it again is 
another thing entirely.

Provided you're willing to accept that any of this makes sense at all, 
that's what the difference is (for that definition of "number" of 
course, which surprisingly is a relatively common one).

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On Sat, 20 Jul 2013 00:02:11 +0200, Kevin Wampler <nob### [at] nowherenet>  
wrote:

> On 7/19/2013 2:32 PM, Stephen wrote:

> 2*w = "count in forever in multiple of two"
> w*2 = "count forever, then when you're done, do it again."
>

I see a light bulb! ;)


-- 
-Nekar Xenos-

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On 19/07/2013 11:59 PM, Nekar Xenos wrote:

>
> How about:
>
> Complex Infinity ^ Complex Infinity
>

Good question. What do you think?

> But I suppose if you can't add them, you can't power them...
>
Who said that? I can't find it in the thread as it is getting long.
I thought you could, if it makes any in ordinary language. Is it a 
property of them having one more dimension?

-- 
Regards
     Stephen

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On 20/07/2013 12:12 AM, Stephen wrote:
> if it makes any in ordinary language

if it makes any sense in ordinary language

-- 
Regards
     Stephen

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