is restricted to the domain {x | x != 0}. Because e.g. when x = 0 and y = 1, the expression then contains a zero in the denominator. Division by zero is "every number, and therefore no single number" because we can use algebra to "prove" that x / 0 equals "anything we want", almost like the how the principle of explosion works.
If you wanted to prove that 0^0 really does equal 1, you would have to prove that the output of the reduction is unique.
If you wanted to prove that 0^0 really does equal 1, you would have to prove that the output of the reduction is unique.