# Are there different sizes of Infinity?

there are an infinity of numbers, and there are an infinity of odd numbers. how can this be? is each infinity a different size?

Update:

Iason Ouabache - Exactly. It does blow my mind.

Update 2:

Duke - yes.

Update 3:

phoenixstarshine - Exactly. Set theory is very confusing to me, but I asked this here precisely because I thought I'd get some different ideas.

Relevance

Want me to blow your mind?

[infinity] + [infinity] = [infinity]

• Anonymous

More than that, there are an infinite number of numbers between 0 and 1, an infinite number between 1 and 2, and this goes on for infinity. Don't think about it too much you'll hurt your head. I believe there have been a few books written on the subject. The Levels of Infinity or some such thing. Just a little reminder that we're not quite as smart as we think we are and there is still a lot for us to learn about the universe.

• There is only one infinity.

You get weird things happening with the infinite. Infinity + 1 = infinity.

Infinity * 10 = infinity.

1/infinity = 0 = 1,000,000,000/infinity

infinity/infinity = something between 0 and infinity, for different conditions.

Infinity is a mathematical concept, not a actual number. I wish people who claimed their deity has infinite knowledge/power/love understood this.

• Actually Infinity is not even a measurement. It is the inability to measure something becouse The definition of Infinity is to be without an end. Thus your "infinity of numbers" and "infinity of odd numbers" is considered nonexistent becouse the counting to get to it will never end and/or wont ever stop. hope this answers your question

it can be an infinity becouse infinity keeps going on.

the size of infinity is incalculable and unreachable, So it isn't even be considered a measurement.

• infinity isn't a number. If there is an infinite amount of numbers meaning that numbers never end than it would be impossible for there to be a finite amount of odd numbers. Infinity doesn't come in a size if it did than it wouldn't be infinite. In order to have size you have to have a boundary to establish it. Infinity by definition has no boundary.

• Anonymous

The sizes of two infinite sets are compared by verifying whether they can be put in one-to-one correspondence with each other. For instance, the set of positive even numbers and the set of positive integers have the same "size" or cardinality because of the correspondence

1 <-----> 2

2 <-----> 4

3 <-----> 6

etc.

On the other hand, it can be shown that no such correspondence can exist between the rational numbers and the irrational numbers, so we say that those two sets have different cardinalities.

See if you can guess how one infinite set is shown to have equal or larger cardinality than another.

• I know this is a math question, so here it goes: a set is infinite if it can be placed in a ono to one correspondence with one of its own proper subsets... for example, the number of counting numbers is the same number as the number of odd counting numbers because you can assign each odd number as first, second, etc. As for different kinds of infinity, there are an infinite number of kinds of infinites, for example, there are more real numbers as there are counting numbers,etc...

• Nope. Infinity is infinity. It helps if you don't think of infinity as a value, but rather as a designation that the set in question has no limit.

• Infinity has no size because size indicates limits, and infinity has no limits.

• Anonymous