I don't necessarily disagree with your point that for the given audience it's not appropriate to rigorously define the different sets of numbers. However, I ab

I don't necessarily disagree with your point that for the given audience it's not appropriate to rigorously define the different sets of numbers. However, I absolutely detest it when teachers just "sweep it under the rug", when they pretend that they just provided a definition when they evidently did not. Like the commenter you replied to, this sort of stuff genuinely threw me off in high school and made me feel like I didn't understand mathematics.