User blog:Cheetahrock63/Hyper operator notations

I was genuinely surprised to find out that no one had proposed a system meant to extend summations and pi notations.

For anyone who doesn't know, these notations create the end result after hyper-operating a set of numbers in a sequence, with $$\sum$$ for addition and $$\prod$$ for multiplication, respectively.

An example for the former would be $$\sum_{k=1}^5 2k=2+4+6+8+10=30$$ and the latter would be $$\prod_{k=1}^5 2k =2\times4\times6\times8\times10=3840$$.

The bases of the notations are the commonly used hyper-operators, addition and multiplication. However, I've wondered if you could extend from there.

Sure, these notations would have zero practical use, but they seem nice and fun for generating very large numbers.

For exponentiation, I used $$\Epsilon$$, making it epsilon notation, as epsilon is equivalent to E, for exponentiation, much like the naming of the sigma and pi notations. The definition of Epsilon Notation is the power created when exponentiating numbers in a sequence. An example is shown on the left.

I got a little lazy when dealing with hyper-operators larger than that, so I just slapped a giant 4 for tetration and a 5 for pentation. Not the best way to approach them, as it opens the possibility of replacing $$\sum$$ with a large $$1$$, which is still technically right, but anyone unfamiliar would think those giant numbers look really silly, and especially when using notations with extremely large hyper-operators, for instance, hyper[10000] (but who even uses them?).

I'm considering making "exponentiation notation" a small $$\epsilon$$ and perhaps the subsequent ones would be the capitalized Greek numerals to solve the issue, but for now, this is what I've got.

Have a good day