User blog:Alemagno12/Ordinals in programming languages part 1: Brainfuck

If we can define w in a programming language, then we can define larger ordinals by using that programming language and w.

In this blog post, I will extend Brainfuck to include w, and see what ordinals we can generate.

Definition
There is the tape with an infinite number of cells, and a pointer which start at cell 0. Each cell starts with a value of 0.

> moves the pointer 1 cell to the right

< moves the pointer 1 cell to the left

+ increases the value of the cell the pointer is on by 1

- decreases the value of the cell the pointer is on by 1

[ does nothing

] does nothing, unless the value of the cell the pointer is on is not 0, then find the rightmost [ at the left of the ] and continue running the code starting from the [ you found

. outputs the value of the cell the pointer is on

To generate w in Brainfuck, we will add one more thing:

w increases the value of the cell the pointer is on by 1