[aeneasmackenzie]

They don’t exist as concepts. A rational number whose square is 2 is (convenient prose for) a formal symbol describing some object. It happens that it does not describe any object. I am claiming that many objects described after the explosion of mathematics while putting calculus on a firmer foundation to resolve infinitesimals do not exist.

List functions like that need to be handled carefully to ensure termination. Summations of infinite series deal are a better example, consider adding up a geometric series. You need to add “all” the terms to get the correct result.

Of course you don’t actually add all the terms, you use algebra to determine a value.