I think this definition is somewhat non-standard for laypeople. Most people think of x^y to be defined as "x multiplied by itself y times" or something similar.

I think this definition is somewhat non-standard for laypeople. Most people think of x^y to be defined as "x multiplied by itself y times" or something similar. By this definition, 0^0 is a convention/shorthand, not a truth. I think the "functions from b to a" definition is useful to note too, though