How Does total vs. partial functions [episode 12] Work?

A total function is like a vending machine that always gives you a snack when you press a button, no matter what button you pick. A partial function, though, is more like a vending machine that sometimes doesn’t have the snack you want, if you pick the wrong button, it might just say “out of order.”

Imagine you have a toy box full of blocks. Each block has a number on it. If you give me a number, I’ll give you back a specific block. That's like a function, it takes something in (input) and gives you something out (output).

Now, if every number from 1 to 10 is matched with one of your blocks, that’s a total function, no matter what number I pick, there’s always a block waiting.

But if some numbers don’t have a matching block, like if the number 7 is missing, and you ask for it, then I can’t give you anything. That means it’s a partial function, not every input has an output, just some of them.