Question

What are the numbers bigger than infinity ?

Answer 1

infinity + 1

Answer 2

2x infinity

Answer 3

no, there is something about cantorset

Answer 4

are you thinking of the cardinality of a set

Answer 5

Yes, I don't know much about it

Answer 6

don't think too much about the cantor set...it will make you crazy ;)

Answer 7

lol

Answer 8

There are no numbers bigger than infinity.

Answer 9

actually , there is

Answer 10

when you are talking about the sizes of sets...there are different levels of infinity

Answer 11

There are, in fact, an infinite number of infinities when thinking about cardinality.

Answer 12

That kind of thinking makes people go mad :(

Answer 13

yes....keep applying the power set

Answer 14

The way to think about it is. Two sets X and Y are said to be of the same cardinal type or have the same cardinality if there exists a bijection between them.

For example, if X = {1,2,3}, Y = {cat,dog,horse}, these two sets have the same cardinality and we call that cardinality 3.

Answer 15

Now consider all the natural numbers, N. We call the cardinality of this set aleph-zero
\[ \aleph_0 \]

Answer 16

It turns out that the integers and the rational numbers also have cardinality aleph-0. So in fact does every lattice
\[ \mathbb{Z}^n, \mathbb{Q}^n, \mathbb{N}^n \]
for every finite n.

But it turns out the real numbers do not have cardinality aleph-0

Answer 17

Instead, it can be shown that the reals have the same cardinality as the power set of N. We call it aleph-1, \( \aleph_1 \).

Answer 18

You can continue stepping up cardinality by continuing to take power sets. For example, the power set of the reals has cardinality aleph-2.

Answer 19

It's worth noting for this notion of infinity that
\[ \aleph_0 + 1 = \aleph_0 - 1 = \aleph \]

If you take the integers, take one of them away or add one more, you still have the same number.

Answer 20

It's also true that if you look at all the even numbers, they also have cardinality \( \aleph_0 \).

Answer 21

james can u come help me?