This is a variant on the question small real numbers.
I have a disagreement with someone about the meaning of "bigger" real numbers.
Say we have the real number $-1.$ Is $0$ "bigger" or "smaller" than $-1$? In other words, should we interpret "bigger" to be a synonym of "greater than"?
This may be considered an "opinion-based" question, but is there a consensus about how to assign meaning to "bigger" or "smaller" (real) numbers?
My interpretation is that "bigger" real numbers have larger magnitude, irrespective of sign. For example, I consider that $-2$ is "bigger" than $-1.$ To avoid ambiguity (we are mathematicians!), I think it better to say/write "$-2$ has a larger magnitude/size than $1$".
Further, I try to avoid using "bigger" or "smaller" with respect to comparing numbers unless it is clear we are comparing their magnitude (e.g. vectors or complex numbers), where we are only comparing non-negative values. I would stick to "greater / less than" or "closer to / further from zero".