What is infinity?

So, this week, I will write about something a bit different. I will be talking about a math concept commonly known as “infinity”.

Most people see infinity as a sideways 8, the common symbol. However, infinity has different levels. The first level of infinity is…….

This is the first “smallest infinity”. This is the number of all natural numbers there are. Also, all even numbers. Also, all odd numbers. Also, all rational numbers. This is the number that is equal to the sum of every single number possible.

But what if you have an ℵnumber of lines, and then you draw one after all those lines?

Would it be a ℵ+ 1? No. It would still be ℵ0, but you just start from the one after. But what if you had to show the lines in the order that it were drawn? Then it would be ω (omega). This number does not contribute to the total, but is after ℵ0. Congratulations, you have just passed infinity. After ω, it is ω + 1, then +2, then so on, then, skipping x2 and so forth, you get ω1. Then, ωω… No problem. This is just ε0. But what if there is a level of infinity, so high, that no amount of lower infinities caould reach it.

 

Such a number is called an inaccessible cardinal. The symbol? θ. This is a number so infathobly large that is would be impossible to reach. Interestingly enough, a shadow of this number has already been found.   ℵ0. Nothing can also reach it from below.

Congragulations. You have reached infinity.

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