Quote from: Leslie on March 02, 2008, 03:02:06 AM
In a mathematically rigorous sense, you can't add or subtract or multiply or divide infinity. Infinity isn't really a number; it's more of a concept.  That said, if you want to try to assign some meaningful values to infinity, I'd use these:

Infinity plus infinity would be infinity. If you have two things that are without end, and you put them together, you're left with something without end.

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Infinity minus infinity is really tough to define! This is usually called an "indeterminate form" in mathematics.

Of course, it's not really so fluid as that: Real analysis yields definitive answers as to convergence, boundedness, and divergence of sequences and series. For example, the limit of the ratio of two divergent (or vanishing) functions can be defined using l'Hopital's rule. Certainly you're correct that in analysis, it's more of a concept that a number in its own right: it's sort of an "extra" number that behaves a bit differently, and basically represents a way that sequences or series can fail to converge -- "For every positive integer n, there exists and M..."

But infinity in the set-theoretical sense certainly is a number -- or more accurately, in infinite class of numbers! (see Cantor's Diagonal argument, which proved the existence of uncountable infinities -- really nifty!)

What kind of infinity? Mathematical infinity, as a religious concept, as a philosophical idea or just infinity per se?

I think that you can use infinity as a concept (as it was said above) by defining a few ideas of how you think it should work, that would be from outside. Regardless, that's a long ways off from actually imagining infinity and truly understanding how it swirls, that's probably impossible.

Imagine the universe as mathematical. And it is in many ways. Imagine prime numbers then as part of mathematics.  If you ask "Is the universe infinit ?", then you could also ask the question "Is there a last prime number ? And maybe there is.

So .......... maybe the universe is not infinit, it is just awfully big making it look like infinit.



Posted on: April 10, 2008, 01:04:27 AM

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Quote from: Alyssa M. on March 02, 2008, 04:15:27 AM

Quote from: Leslie on March 02, 2008, 03:02:06 AM
In a mathematically rigorous sense, you can't add or subtract or multiply or divide infinity. Infinity isn't really a number; it's more of a concept.  That said, if you want to try to assign some meaningful values to infinity, I'd use these:

Infinity plus infinity would be infinity. If you have two things that are without end, and you put them together, you're left with something without end.

...

Infinity minus infinity is really tough to define! This is usually called an "indeterminate form" in mathematics.

Of course, it's not really so fluid as that: Real analysis yields definitive answers as to convergence, boundedness, and divergence of sequences and series. For example, the limit of the ratio of two divergent (or vanishing) functions can be defined using l'Hopital's rule. Certainly you're correct that in analysis, it's more of a concept that a number in its own right: it's sort of an "extra" number that behaves a bit differently, and basically represents a way that sequences or series can fail to converge -- "For every positive integer n, there exists and M..."

But infinity in the set-theoretical sense certainly is a number -- or more accurately, in infinite class of numbers! (see Cantor's Diagonal argument, which proved the existence of uncountable infinities -- really nifty!)

Yes you can divide infinity ! You really can.  00 divided by 00 can be any number.

lim sin(x) /n  = 6, when n -->oo (infinity)

Proof: Cancel the n in the numerator and denominator and remove the parenthesis from x.