> The point is that in elementary school arithmetic, you define addition, multiplication, subtraction, division, decimals, and equality, but you never define ".

> The point is that in elementary school arithmetic, you define addition, multiplication, subtraction, division, decimals, and equality, but you never define "...". Until you've defined "...", it's just a meaningless sequence of marks on paper. You can't prove anything about it using arithmetic, or otherwise. Sure, but the point of "elementary school" arithmetic is not "elementary" arithmetic, as a mathematician would define it :-) The goal is to teach people to reason by matching patterns. Deductive/Inductive reasoning can slowly proceed from that, as they try to frame their intuition for patterns into increasingly more general abstractions.