infinite numbers

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 ℵ<sub>0</sub>. We call this symbol ℵ<sub>0</sub> ``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

>>21
Different process to reach them. An example with fictional banks and money.
Like if you had 2 banks each started with 100$ account of different percents rates.
Now imagine one bank gives you +110% daily but another multiplies your money x1000.
They both can reach "infinite money" but if we compare them by yearly rate,
the progress is much faster on the second bank.
At any point in time, the second bank account will be much larger than first.