Thread:Exermis/@comment-40263239-20200211074715

First of all, the smallest infinity is aleph-0, or countable infinity. It is how many natural numbers there are, and how many rational numbers (fractions) there are. Weird? Well, every fraction can be corresponded to a natural number. Just list all the fractions in an infinite square where each row have the same numerator and each column have the same denominator, and count from any fraction and spiraling outwards. The first fraction you count is corresponded to 0, the second to 1, and so on.

But what is the smallest uncountable infinity, or aleph-1? It is how many real numbers there are, how many points there are on a line segment, how many points there are on a line, and how many 4-D universes there are in a 5-D space. I'll first prove that there are more real numbers than natural numbers and fractions:

Let's say someone made a list of every real number, which could only be possible if the amount of real numbers and natural numbers is the same, because you can correspond each real number to a natural number by counting down the list. Now, every real number can be represented as an infinite decimal (if it is finite, just add an infinite tail of 0's behind). I will now construct a real number that is not in the list.

First, I'll draw a diagonal line from the first digit of the first number to the second digit of the second number and to the third digit of the third number and so on. Every digit this line crosses will be a digit of a new number. Then, I add 1 to every digit, and if the digit is 9, I turn it to 0. This number that I just constructed is not in the list, because it is different from the first number at the first digit, from the second number at the second digit, and so on. That is a contradiction, so the list is impossible, and there are more real numbers than there are natural numbers.

Every real number corresponds to a point on the number line. Every 4-D universe in a 5-D space can be described just using its position on the fifth dimension, which is a real number. So, there are aleph-1 4-D universes in a 5-D space.

The requirement for Low 1-C is "This rating can be reached by 5 and 6-dimensional constructs and spaces when they are either of an infinite (or otherwise non-insignificant) size or portrayed as qualitatively greater than lower-dimensional objects in their setting, or alternatively, one can also qualify for its lower end by creating and/or destroying an uncountably infinite number of universes."

The part after the "also" is equivalent to the part before the "also". Why? In a 5-D space of non-zero volume, there must be a non-zero distance on the fifth dimension between one end of the space to the other. Let's say that the 4-D universes are aligned on this fifth dimension (if not, just rotate them). Every 4-D universe corresponds to a real number that is its position on the fifth dimension. If these real numbers do not cover the entire number line, the tangent function will stretch them to cover the entire number line. And I had already proved that there are uncountably many real numbers, so there are also uncountably many universes in any 5-D space of non-zero volume.

If your character can only destroy countably infinite universes, the 5-D volume covered by them is always 0, and that is only 2-A, not Low 1-C. 