Cardinality in mathematics
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It a count of the number of elements in a set.
A set contain 3 items has a cardinality of 3. A set containing 10 items has a cardinality of 10.
Now, I am assuming that you are actually asking what it means with respect to infinities. And yes, there are different “sized” infinities.
If you look at the set of all integers, it is infinite. You can always just add 1 to the highest integer, or subtract 1 from the most negative integer and get a new member of the set. This is defined as having a cardinality of aleph-0 (which goes with the infamous drink song, Aleph-0 bottles of beer on the wall, Aleph-0 bottles of beer. You take one down, and pass it around Aleph-0 bottles of bear on the wall).
How can anything be larger than infinity?
Consider the set of real numbers. Are there more real numbers or integers? They’re both infinite so the sets must be the same size! Consider this, however…
Order both sets in increasing size (that is probably how you imagine the set being ordered anyways although technically order is not important in sets).
Between any two elements of the set of integers there is a finite number of elements. The number may be very large but if given enough time you could count them.
Let’s do the same thing with the set of real numbers. Houston, we have a problem! The number of elements between ANY two elements is infinite. We cannot count all the elements between ANY two elements. This is an uncountable infinity, and is a larger infinity than one with a cardinality of aleph-0. It’s cardinality is greater than aleph-0.
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