Saturday, August 13, 2005

Maths with infinity

When you take a maths class you will be taught by the teacher that infinity divided by infinity is not 1, they may say there is no answer or that that it is indeterminate.
Actually that is just lazy logic. Infinity is not a "number" per se, it is a class of numbers as a result a specific example divided by another specific example does have an answer we just donâ€™t know what it is until you explain more detail.
It is basically the same as me asking you what is the answer to "a number I just thought of divided by another number I just thought of" (by the way the answer was 2).

Thus the terminology that we use "infinity" obscures information. Thus infinity times 2 is infinity but it is not THE SAME infinity. In maths it may be next to impossible to identify these infinities and thus we may say the answer is indeterminate but this is not a function of infinity it is a function of us not knowing the question.

Here is a link that explains it a bit

http://mathforum.org/dr.math/problems/parkinson10.26.html

I understand at times cancelling of infinity is used very carefully to solve advanced physics problems.

Nigel Kearney said...

NOOOOO!!!!

There are multiple 'infinities' of different sizes, but a sentence such as "infinity times 2 is infinity but it is not THE SAME infinity" is incorrect.

The set of all integers is exactly the same size as the set of even integers.

The proper way to compare sizes is to say that the size of A is less than or equal to the size of B, if and only if there is a mapping from every member of A to a unique member of B.

e.g.

A = {0,1,2,3,...}
B = {0,2,4,6,...}

There is a mapping consisting of {(0,0),(1,2),(2,4),(3,6)..}

And there is the corresponding reverse mapping. Therefore the size of A is less than or equal to the size of B, and vice versa. So the two sets are the same size.

7:17 PM
Genius said...

I agree they can be matched but that doesnt mean they are the same. It is clearly true because..

infinity /infinity is described as being indeterminate - if you were right infinity over infinity would be one.

your next argument is probably anythign that happens at the infinite level doesnt effect anything that happens at the non infinite level.

But
1) That sounds ridiculous
2) I have heard of infinities being cancled in physics equasions
3) If you use the limit n n--> infinity and divide by somthign like limit 2n n-->infinity if you have propoerly defined your infinities you will find that it converges as you would intuitively expect not as you are implying here.

7:48 PM
Genius said...

also
a square is infinitely larger than a line BUT turn a square into a like double the length of a line and make it into a square and it will still make a bigger square than before even if you cant define the size of the square in a one dimentional universe.

8:33 PM
Valefar said...

I'd agree with Genius on this one, at least his answer sounds the most right.
I'm just a run of the mill college student, but we 'disarm' infinities all the time in Calculus.

1:42 PM