If nothing can exceed infinity, then how does THIS compare? -- Infinity to the infinite power, factorial.?

Question

And if you're willing to tackle that, please also consider this:

An object of given mass strikes an immovable object at light-speed minus 1 cm/sec. How does the energy released from that impact compare to the energy that would be released if TWO objects of the *same* mass were each travelling TOWARD each other, and collided head-on, wherein each object were travelling at lightspeed minus 1 cm/sec.?

Answer 1

The first case is just half of the second case: one mass hitting an "immovable object" is just like that same mass hitting it's opposite going at the same rate.

So whatever is going to be released, will be doubled for the second case.

Oh, about infinity to the infinite power: These are just words. If you want to get serious about transfinite numbers, look at some of the references.

Answer 2

The answer to your second question is that the enery released for two masses will be double that released for one (at least in the frame of reference described).

For the first question, you have to specify which of many versions of 'infinity' you are wanting. For example, if you are doing limits where f(x) and g(x) both go to infinity, then f(x)^g(x) will also go to infinity, as will Gamma(f(x)), where we use the Gamma function instead of factorials because that is the natural generalization.

If, on the other hand, you are talking about cardinality, the answer depends on which infinite cardinals are used as well as what axioms for set theory you assume. . If A and B are cardinal numbers, A^B is the cardinality of all functions from B to A. If A and B are both countable infinite, then A^B has the same cardinality as the set of real numbers. Factorials are essentially defined via permutations and A! turns out to be the same as 2^A for infinite A.

For ordinal numbers, the definition of exponentiation is done inductively, so omega^omega is a countable ordinal that is the next after omega^n for all finite n.

Answer 3

"If nothing can exceed infinity" is WRONG.

As some of the answers suggest, the infinite number of positive integers is exceeded by the infinite number of real numbers.

Cantor's Theorem implies that there is no largest infinity by showing that if A is any infinite set, one can construct an infinite set B such that B "is larger than" A. Here, "is larger than" means it is not possible to put the elements of A into a one-to-one correspondence with the elements of B, but there is a proper subset of B which is in
1 - 1 corr. with A.

Thus, infinity (B) exceeds infinity (A).

Answer 4

Infinity is not a number. You can not use it in calculations.
There are at least two different kinds of inifinity
Countable infinity: 1,2,3,4...
This goes on foreverer.

The other is the number of points on the number line between 0 and 1.
1.001, 1.002,1002.
But there are also an infinite number of points between 1.001 and 1.002
like 1.0011, 1.0012, 1.0013
But there also an infinite number of points between 1.0011 and 1.0012.

this is a much larger kind of infinity and is called uncountable.
Cardinality is a term that describes the type of inifinity.

Answer 5

infinity is just a word since mankind cannot quantify it.