# How should one rank a combination of positive and negative numbers from smallest to largest?

I thought size was the distance from zero, in which case ordering {-1, 2, -3} would be {-1, 2, -3}, but I saw it ordered as {-3, -1, 2}. Which method is correct?

• Rank the temperatures $-1, 2,-3$ from coldest to warmest. – André Nicolas Jan 11 '15 at 2:00
• Perhaps the terminology 'least to greatest' is preferable (clearer). – paw88789 Jan 11 '15 at 2:07

While "size" is not a formally defined property for real numbers, we do have the notions of order (whether $x<y$) and magnitude (whether $|x|<|y|$). Whether size should refer to order or magnitude is somewhat open to preference, but in my experience everyone considers it to mean magnitude.
I think the most convincing argument for this interpretation is that we often talk about large or small complex numbers, or vectors in $\mathbb{R}^n$. In these settings, we're clearly talking about magnitude--no order exists. Since the real numbers are embedded in these spaces in a very natural way, it makes sense to define "size" on the reals to be consistent with its meaning in the other spaces.