It can't be compared with aleph-null. Why Doesn’t Infinity Count? Perhaps not surprisingly, this new infinity—the cardinality of the set of real numbers ℝ—is called ℵ 1. Infinity exceeds the boundaries of any real or natural number. Smaller than infinity, but really big numbers each. By the definition of aleph numbers, there is no such thing as aleph-1.5. You are using aleph numbers incorrectly. Essentially Skewe’s number proves that a number “x” exists that violates this rule, assuming that Reimanns hypothesis is true then that number “x” is less than 10^10^10^36, (most numbers are) the first of Skewe’s Numbers, much bigger than a googolplex, noted because of the extra tower. This number is larger than infinity to its own power, larger than a power tower of infinities infinitely high ... it simply defies description. Lets count from one to a a million, a googol, Graham’s Number… all the way till infinity, and even how to count beyond infinity, into the uncountable infinities! At first it seems impossible, nightmarish. I think what you are refering to is actually the beth numbers, where each beth number is defined as the cardinality of the power set of the previous one with beth-0 equal to aleph-0. But as you probably figured, infinity doesn’t really count. There are no numbers bigger than infinity, but that does not mean that infinity is the biggest number, because it’s not a number at all. Even though infinity is not a number, it is possible for one infinite set to contain more things than another infinite set. So at last we have finally found a larger infinity than ℵ 0! aleph-1 is the infinity bigger than aleph-0. So that aside, what is the biggest number? He stumbled upon it by accident. We journey to see what amount of quantity for the all the people on earth, all the ants on earth, all the atoms in your body, all the stars in the universe and beyond. In fact, Cantor showed, there are more real numbers packed in between zero and one than there are numbers in the entire range of naturals. It is the largest number ever used to solve an actual problem, and suffice to say there are no words to describe its size. If such were true, Graham's number would take the #1 spot. That is to say, it’s actually a lot easier to consider infinity as not a number. What is the smallest number in the world? Cantor did not set out trying to prove there was a larger infinity. It is often denoted by the infinity symbol ∞.. It’s the second transfinite cardinal number, and our first example of a bigger infinity than the ℵ 0 infinity we know and love. Yet it's existence seems inescapable. Hence, 27 is a real number, as is π, or 3.14159….) There are numbers so large we believe them to be bigger than infinity. Infinity represents something that is boundless or endless, or else something that is larger than any real or natural number. Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions among philosophers.
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