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Comment by baddox | Hacker News Reader

Given a complex number a + bi, the square root of a^2 + b^2 is called the norm. The norm shouldn't be thought of as a measure of the "size" of a complex number, since complex numbers are not well-ordered. It makes little sense to say that 2 + 3i is equal to 3 + 2i.

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Why wouldn't you be able to call it size? Equal size doesn't imply equality elsewhere in mathematics or elsewhere in the world (Jimmy and Paul are the same height, so they must be the same person?).

Two people of equal height aren't the same person, so it would be odd for an article to claim that the way to convert a person to a real number would be to simply measure their height, and even odder to call that the "size" of a person.

     It makes little sense to say that 2 + 3i 
     is equal to 3 + 2i

As the article correctly points out the norm is "the distance from 0". 2 + 3i is not equal to 3 + 2i, but both numbers are on the same circle.

It is generally considered in mathematics that a norm is used to describe length, size, or extent.

This may just be a difference in terminology, but I'm not familiar with mathematicians calling the norm of a complex number its "size." To me, if you call the norm the size, then you could say that one complex number is larger than another, which I believe is nonsensical.

Of course, you could just define a relation < on the set of complex numbers by "x < y if and only if norm(x) < norm(y)". This relation is obviously trichotomous, and it could be considered an ordering of the complex numbers. In my experience, however, this assumption is generally not held or used by mathematicians.

You are correct. From what I could gather from reading that write-up, "size" is used to mean the magnitude of a number.

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