Question

What is the magnitude of numbers all about?

Answer 1

See below.

Explanation:

This is quite a big topic that I will try to explain simply but not completely here.

Put simply, "magnitude" of numbers refers to their size.

First, if we limit ourselves to the real numbers:

Then the magnitude of some `x in RR = absx`. That is the size of `x` without concern as to whether it is negative or positive.

If we now extend to complex numbers:

Then the magnitude of some `z in CC= a+ib`
where `{a,b} in RR` is `sqrt(a^2+b^2)` which is the absolute value of `z` on the complex plane.

This concept can be extended further into other spaces, but in all cases the fundamental concept of magnitude is simply one of size - usually relative to other objects in the space.