They are well-defined now, but when Leibniz and Cauchy were working with them, they were not, and used carelessly could lead to errors. Their "solution" was to

They are well-defined now, but when Leibniz and Cauchy were working with them, they were not, and used carelessly could lead to errors. Their "solution" was to just pretend those errors didn't happen ("don't do that, then") instead of trying to come up with a consistent system of rules for infinitesimals.