User blog:MilkyWay90/Math number

Let's create a "math language" called N.

In N, you can: Add (F(x, y) = +(x, y))

Subtract (F(x, y) = -(x, y))

Use natural numbers (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, ...)

Recurse (F(x, y) = F(x, -(y, 1)), F(x, 0) = +(x, x))

Variables (a0, a1, ..., b0, b1, ..., z0, z1, ..., aa0, aa1, ...)

Other functions (A(x) = x, F(x) = A(x + x))

Equality (equal sign, but no greater than or less than or not equal)

To define a function, do Function(v0, v1, v2, ..., vn) = (expression)

Note: Addition and Substraction can only hold 2 arguments. Use +(2, +(2, 2)) instead of +(2, 2, 2)

Now let's get into symbols!

F(x) = +(x, x) has 6 symbols because F(x) is 2 symbols (F, and x), = is one symbol, +(x, x) is 3 symbols (+, x, and x)

So Functions, natural numbers, equal signs, variables, etc. are symbols.

So here is my function:

Math(x) = The largest F(x) that can be formed by N with less than or equal to x symbols with the absolute value of all natural numbers in N being less than x. If all possible F(x)s are ill-defined (ex. F, x =, =y, F(y), etc.), then Math(x) = 0.

I define Math Number to be \(Math^{{}^{100}10}({}^{10 ^ {100}}10000000)\)