2012/002) Why must you flip the inequality symbol when you divide by a negative number?

this follows from the analysis below

say x < y

now subtract x + y from both sides

x - (x+y) < y - (x+y)

or -y < - x

hence dividing or multiplying by -1 changes the sign

divide by a positive number does not change the sign
so divide by - number changes sign

(this being the last entry of the year this was a small but useful analysis)