Suppose you want a compact, clever formula for the function: f(x)=1 if x!=0, f(x)=0 if x=0 If 0^0 were defined as 0, you could write the above function as f(x)

Suppose you want a compact, clever formula for the function: f(x)=1 if x!=0, f(x)=0 if x=0 If 0^0 were defined as 0, you could write the above function as f(x)=x^0. With 0^0 defined as 1, you're forced to write something like f(x)=1-0^|x| (absolute values to avoid division by zero), a bit more complicated. This is silly though, and of no importance anywhere.