That’s an add-on: first consider strictly positive integers.

The deal here is “big and little,” which is a big deal.

What makes it a big deal is that everybody knows about big and little, and that means everybody knows something really important about mathematics.

In math-speak, the order relation between positive integers is “little comes before big.”

The natural parallel is that kids are little *before* they are big.

Zero is easy: littler than littlest is nothing.

Negative numbers are trouble.

What mathematics gives you is machinery to deal with trouble.

The mathematics “machine” that handles negative numbers is “the number line.”

On the number line, the order relation among positive integers is “left comes before right.”

Mathematics is about “extending ideas.”

The left-comes-before-right idea “extends” to the entire number line.

Mathematics often produces surprises.

The surprise that comes from extending left-before-right to negative numbers is that negative-big comes before negative-little.

And 0>-1, which is a surprise if it says that zilch is bigger than something, but not a surprise if it says that zilch is bigger than less-than-nothing.

Maybe it’s illuminating to divide the number line into three regions: nothing, something, less-than-nothing?

An important idea is that the order relation between integers is “transitive.”

What it means:

if A