Infinity

[Buffy]

-_-

 

Mr. Craig is sooooooooo smart!

 

What I really have been waiting for you to comment on Craig is my post above concerning the *application* to probability...I'm still fascinated about how that 1 in the numerator gets you one item that's counter to the "infinite" set...

 

You're on vacation and rested: expound!

 

The opposite of a correct statement is a false statement. But the opposite of a profound truth may well be another profound truth, :hihi:

Buffy

[freeztar]

Thank you Craig!

 

I was about to vehemently object to this whole 0.[9]=1 principle, but your last post made it clear. It *is* philosophical. This makes me wonder what other mathematical abstractions can be lumped into the philosophy category?

 

Good stuff!

[Qfwfq]

How's that?

Actually it's an algebric inversion of the same thing. True, it is the special case of how to show what the summ of the geometric series is, but I wasn't expecting Buffy to need to be taught that, or for her to call it, uhm, definitional! :hihi:

 

Note however that we are both "just leaving the [imath]lim[/imath] stuff out" and that it is shaky to say that it's simple plain algebra. Without topology one couldn't show the series is convergent at all. The exact same algebra could be applied to a divergent geometric series, getting the same formula I posted back there; obviously it isn't valid.

 

Oh you know I'm just playing here dear...

You know I am too! :D

 

But from what you say, perhaps it's the notion of topological sum which you find unsatisfactory?

[lawcat]

I have no beef with approximations for practical purposes. Infinity is chaos and uncertainty. Thus we have limits for very large numbers. I personally don't think infinity can exist in real universe, otherwise there would be much more instability and distortion. But since we must deal with great quantities in some practical areas, it makes sense to approximate, or limit infinity as the case may be.

[Buffy]

I have no beef with approximations for practical purposes. Infinity is chaos and uncertainty. Thus we have limits for very large numbers. I personally don't think infinity can exist in real universe, otherwise there would be much more instability and distortion. But since we must deal with great quantities in some practical areas, it makes sense to approximate, or limit infinity as the case may be.

Yah, that's fine, but this is Mathematics: whether it is "practical" or not is completely irrelevant!

 

Real mathematicians all have a disgusted look on their faces and are rolling their eyes right now....

 

Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true, :)

Buffy

[lawcat]

Lol!

 

I thought grants were rooted in a belief that the research will have some practical application. (grazing in a field between practical and imaginary is dangerously religious in nature.)