AI Tutor
Imagine two freezers: one is set to βˆ’2∘F-2^\circ\text{F} and the other is set to βˆ’10∘F-10^\circ\text{F}.
The freezer at βˆ’10∘F-10^\circ\text{F} is much colder, which means βˆ’10-10 is actually a smaller value than βˆ’2-2.
On any standard number line, the golden rule never changes: values further to the right are always greater, and values further to the left are always less.
So how do we write this mathematically using comparison symbols?

Comparing Two Negative Integers

We use the inequality symbols << (less than) and >> (greater than), where the open mouth always points toward the greater number.
Let's compare βˆ’6-6 and βˆ’1-1. Because βˆ’1-1 is to the right of βˆ’6-6 on the number line, we write βˆ’6<βˆ’1-6 < -1 (or βˆ’1>βˆ’6-1 > -6).
It is easy to get tricked because 66 is bigger than 11, but with negative numbers, being further below zero makes a number smaller.
Think of it like debt: owing \6meansyouhavelessmoneythanifyouonlyowemeans you have less money than if you only owe$1$.
What happens when we need to put a whole messy list of positive and negative numbers in order?

Ordering Mixed Sets of Integers