Comment by Gabriel54

As someone who (almost!) has a PhD in mathematics I'm going to have to call you out on this point. You are thinking like an engineer and talking about precision, but this is mathematics, not engineering. We make no distinction between the "real" number 3, the "complex" number 3, and the "whole" number 3. The number 3 lives in each of these universes as the same object (so to speak) because these sets (whole, real, complex) numbers are included in one another. Writing 3.0 is a representation for 3 just as 2.9999... is a representation of 3. Perhaps the bigger question we should be asking here is what was the purpose of all of this discussion? I've seen such petty treatment by teachers all the time and it always discouraged me from pursuing math until I met professors in university who actually tried to teach us something interesting and beautiful about math. This question could have led in that direction actually with a discussion of different kinds of numbers but unfortunately many math teachers in the US are not capable of this, or are too discouraged by the other craziness in schools to have the energy for such conversations.