Is there many kinds of infinity?

[little boy]

Is there many kinds of infinity? e.g. some infinity is larger that other infinity

 

such as lim x->0, 1/x=infinity and lim x->0, 2/x=infinity

 

both are equal to infinity, but actually the "second infinity"=2*"first infinity"

Edited September 17, 2011 by little boy

[mathematic]

Infinity is not a number, so your example doesn't really have any meaning.

 

There is a part of mathematics where different sizes of infinity are discussed, but it is not related to your example.

 

http://en.wikipedia.org/wiki/Cardinal_number

 

http://schools-wikipedia.org/wp/c/Cardinal_number.htm

 

Either of these may be a good place to start.

[DrRocket]

Is there many kinds of infinity? e.g. some infinity is larger that other infinity

 

such as lim x->0, 1/x=infinity and lim x->0, 2/x=infinity

 

both are equal to infinity, but actually the "second infinity"=2*"first infinity"

 

Your example fails to exhibit the fact that there are in fact many infinities.

 

But if you would care to research the topic of cardinal numbers you will find that there are infinitely many infinite cardinals, which measure the size of infinite sets.

 

The cardinality of the real numbers, for instance, is strictly larger than the cardinality of the natural numbers, though both are infinite sets.

 

However 2 x any infinite cardinal is just that same infinite cardinal again.