User blog:GamesFan2000/My Googological Function

Hypernova Array Function

A mathematical function created by me

In mathematics, a function is any defined series of symbols that can be used to describe a number. Array functions are commonly represented as {a, b, …n}, with every new entry vastly increasing the magnitude of the array. The most famous of these is Bowers’ Exploding Array Function, or BEAF. This function is extensive in how far you can take it, and extremely useful for building absolutely unfathomable numbers. But BEAF still has its limits, and today I’m going to define a function that will utterly destroy BEAF if expanded enough. This is the Hypernova Array Function, or HAF.

Before we define this function, it should be noted that all hyper-operators have another hyper-operator directly after it that tells you to repeat the previous one. Beyond exponentiation(a^b), we have tetration (a^^b, or repeated exponentiation), pentation (a^^^b), and so on and so forth. The order of operations is also important. For the purposes of this function, all equations are solved in order of parentheses, strongest hyper-operator, and in order of strength down to the weakest hyper-operator, where strength is defined as how big the resulting numbers are when the same integers are used for each hyper-operator.

In a hypernova array, the following steps are to be taken for a basic array:

{a, b1, b2, n}, where a is the base, n is the roof, and b is a floor, for all b. The array can have any number of floors.

{2, 4, 3, 3}

Start by taking a and doing the following:

a shall exponentiated by itself, repeated a times. 2^2^2=2^4=16

Take the result and multiply it by itself, repeated a times. 16X16X16=16^3=4096

Take the result and add itself to it, repeated a times. 4096+4096+4096=4096X3=12288

The amount of hyper-operations you will use per entry is 3o, where o is the ordinal number that corresponds to that entry’s spot in the array.

Take the final result from the first set of operations and hexate it to b1, pentate the result to b1, tetrate the next result to b1, and so on until you finish the addition.

((((((12288^^^^4) ^^^4) ^^4) ^4) X4) +4

Repeat the process for all entries using the 3o formula to determine the number of hyper-operators needed.

You can use entire arrays as entries in the main array.

{5, {5, 6}, 7}

These are to be solved before you solve the main array, using hypernova array rules.

If an array seems too unwieldy, you can represent it a different way:

{a(b)}, where a is the value of the entries and b is the number of entries.

{10(12)}={10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10}

You can also express the value of the entries and the number of entries using individual arrays, and use multiple condensed sections in the same array, to create some terrifyingly massive numbers:

{{30(60), 20({80, 100})}, 400({50(300)}), {15, 20}}

If that’s not big enough, you can use an entirely different expression:

{a/}, where the value and number of entries is a.

{a/b}, where the value and number of entries is a^b.

{10/100} (Yes, that is an array where the number of entries and the value of the entries are both equal to a googol.)

{a/b/c}, where the value and number of entries is a^b^c.

{a//b}, where the value and number of entries is a^^b.

If individual arrays are used in combination with the slash, they must be solved before you exponentiate.

{{50/40}, 80/90(85), {200, 100(15)}/{10///10}, 80//10////50}

You can use a subscripted number to represent the amount of slashes, i.e. /100.

Repeatedly putting arrays within arrays in conjunction with the use of slashes will create multiverse shattering numbers. But we’re not done yet.

{a’}, where the number of slashes is a, and the resulting array is {a/a}. The rules for multiple apostrophes, two numbers surrounding one apostrophe, and individual arrays are the same as the rules for slashes, and they will apply for all later extensions of the hypernova array function.

{[a, b]}, where the number of individual arrays and the value of each array is equal to the expression within the square brackets. Square brackets can contain each other and will use the result of the brackets immediately before them.

{a|}, where the number of square brackets is equal to a and the value within the brackets is {a}.

{a¦}, where the number of vertical lines is equal to a.

{a•}, where the number of separated vertical lines is equal to a.

{}, where every previous extension of the function must be used a times, and then repeated a times(the number of entries is equal to a).

That’s as far as I’m willing to define this function. It may seem like this is pointless, but math contains plenty of pointless things. You can keep expanding on what I’ve shown if you want. I just did this for fun, and I don’t intend for this to be taken seriously.