this doesn't make sense to me, smart people? (infinity)

[daviddem]

Forget talking about "bigger", "larger", "more", "size", etc when talking about infinite sets because these concepts don't really make sense for infinite sets.

If you take something out of this, it should be that the infinite sets of the same family as the natural numbers are "countable" or "listable". You can decide some criteria to order the elements one way or another, and start writing a list of them. This list is never ending, but as you go you will never miss an element:
0
1
2
3
etc
I didn't miss any natural number so far, and I won't for as long as I continue.

You can't do that with infinite sets of the same family as the real numbers. These sets are "uncountable" or "unlistable".

However it is mathematically true that if you define some arbitrary symbol N0 to designate the cardinality of the natural numbers, it is then possible to prove that the cardinality of the real numbers is equal to 2^N0, and this is always bigger than N0.

So the cardinality of the set of all real numbers is greater than the cardinality of the set of all natural numbers, whether you like it or not.

And in math, another way of saying that the cardinality of a set is greater than the cardinality of another is to say that the first set is more numerous than the second. Two sets that have the same cardinality are equinumerous.

So while both the set of natural numbers and the set of real numbers are infinite, they are not equinumerous.

[rong]

Forget talking about "bigger", "larger", "more", "size", etc when talking about infinite sets because these concepts don't really make sense for infinite sets.

If you take something out of this, it should be that the infinite sets of the same family as the natural numbers are "countable" or "listable". You can decide some criteria to order the elements one way or another, and start writing a list of them. This list is never ending, but as you go you will never miss an element:
0
1
2
3
etc
I didn't miss any natural number so far, and I won't for as long as I continue.

You can't do that with infinite sets of the same family as the real numbers. These sets are "uncountable" or "unlistable".

However it is mathematically true that if you define some arbitrary symbol N0 to designate the cardinality of the natural numbers, it is then possible to prove that the cardinality of the real numbers is equal to 2^N0, and this is always bigger than N0.

So the cardinality of the set of all real numbers is greater than the cardinality of the set of all natural numbers, whether you like it or not.

I agree with the uncountable part. I agree that cardinality of the set of all real numbers is bigger. What I dispute is the interpretation that this means one infinity is.bigger than the other. And further I'm stating that if that's what this branch if mathematics states then it shows it is unable to deal with infinite sets.