Name: ribbon 2017-07-05 15:15
So you see, there are two infinities: one of integers and one of real numbers. The latter is larger than the former, even though there is an infinite number of integers keep counting and eventually you'll get to any. This is not so with reals, because there are an infinite number of real numbers in a single integer you can never progress past one. We don’t know any infinite ``numbers'' yet, but we can see that some infinite ``number'' must exist in order to describe the number of elements in the set of real numbers. So we decide to just give this infinite ``number'' a name. We call it ℵ0. We call this symbol ℵ0 ``aleph-null.'' Aleph is just the first letter in the Hebrew alphabet, and null just refers to the 0 subscript. ℵ0 is not a number in the way that 5 or 12 million or 3.79384509 is a number. We cannot count ℵ0 out on our fingers, we need to just become comfortable with the idea that ℵ0 is simply DEFINED to be the cardinality of the natural numbers, which is a certain infinite "number". Because ℵ0 is infinite, it is very large, so large that we cannot write it down except to write ℵ0