The infinite archive

[Resha Caner]

I saw a very interesting thread in the archive on infinity. Why was it archived, which basically killed the thread?

 

I would have replied, but I can't.

[Mr Skeptic]

Why don't you link to it and add your thoughts here?

 

I don't know whether they can get un-archived.

[Resha Caner]

Alright, I'll do that.

 

http://www.scienceforums.net/forum/showthread.php?p=330477#post330477

 

The thread seems to have left off discussing whether any arithmetic operations can be done on infinity. It hurts my head a little, but I think the statement is correct that no operation can be done on infinity - basically because it is not a quantity.

 

However, operations can be done that involve infinite concepts - a subtle but important difference.

 

In calculus, an example is L'Hopital's Rule, where you can compare the rate at which two quantities approach infinity. In some cases, the result is a finite quantity, which is the beginnings of the concept of "levels of infinity".

[Mr Skeptic]

I think it would be fair to say that you can do operations on infinity so long as you know where you got the infinity from? But then arguably the operations are actually being done on the infinite series. An interesting concept.

[Resha Caner]

Maybe it's just a semantic argument. But, if you have an example of doing an operation on infinity itself, I'd like to see that.

 

In many cases I'll bet you'll find it's just shorthand for the more rigourous and proper process. If I recall, the idea of "infinitesimal" in calculus is technically wrong, though much easier to grasp conceptually than things like delta-epsilon proofs. And, in the end, both give you the same answer.

 

Engineers take improper short cuts all the time that get us the right answer. Scientists hate us for that.

[Cap'n Refsmmat]

I moved that thread over to the Math forum. If you want to continue the discussion there you can.