The "avoid special cases" argument comes up a lot in math too. For example in combinatorics, some people define 0^0 = 1, so that lots of formulas with "if x ==

The "avoid special cases" argument comes up a lot in math too. For example in combinatorics, some people define 0^0 = 1, so that lots of formulas with "if x == 0 then this else that" just collapse into "that". (Other people insist on inventing a different symbol for this "special exponentiation", but I think that's unnecessary myself.) For the same reason, an empty sum is defined as 0 and an empty product as 1, so your base cases of some inductions don't require an extra "if".