I am in the middle of constructing a theory that is specifically focused on iterations. The symbol for iterations is uppercase phi. It is like a sum but instead of adding them together, you take iterations of the numbers. So, you use n in the equation, and if n is equal to let's say, 5000 you replace n with 5000 in the next iteration. But the beauty of this theory is that you do not have to take an infinite number of iterations. you just have to reason your way out of an iteration. Let me give you an example. Say we are taking an iteration of x to the power of n over n to the power of n. We can reason that n to the power of n will reach infinity, so we have something over infinity. Because n to the power of n will reach infinity, n will also reach infinity. If we take x to the power of n, we can see that it is infinity over infinity. In this theory, to avoid loopholes, we treat infinity as a number. What happens if that infinity over infinity is equal to one. So that iteration equation is equal to one. Another example is the square root of n over the cube root of n. Now, this is a trick question actually. See, what happens is that you might say it will be one because both of them reach zero and zero over zero is one. But no, it is actually infinity because cube root n will reach zero first thereby making it infinity. That is what I have so far. How can I improve this framework?

 

4 minutes ago, grayson said:

I am in the middle of constructing a theory ...

... should have been posted in the Speculations, by definition. Leave my stream alone.

28 minutes ago, grayson said:

I am in the middle of constructing a theory that is specifically focused on iterations.

I am sorry to rain on your parade, but such theory already exists (and has done since Newton's forward and backward difference formulae)

 

Iterative methods are also called recursive methods in Analysis and Calculus and come in two flavours : Linear and Non linear recursion.
There are also iterated integrals (Fubinis Theorem) and iterated series.