One line for all the reals
Draw a horizontal line, mark a point as 0, and step off equal gaps to the right for 1, 2, 3, … and to the left for −1, −2, −3, …. That is the number line, and the beautiful fact is that every real number sits at exactly one point on it — including the fractions between the integers and the irrationals like sqrt(2) ≈ 1.414. A signed number is just a number together with its direction from zero: right is positive, left is negative.
Reading order off the line
The line gives you the order relation for free: the number farther to the right is the larger one. So 3 > 1 and −1 > −4, because −1 sits to the right of −4. The inequality symbols < (less than) and > (greater than) always open their wide mouth toward the bigger number. This is where many learners stumble: with negatives, the one that looks “bigger” by digits is often the smaller number. −9 < −2, even though 9 > 2.
←——•———•———•———•———•———•———•———•———•——→ −4 −3 −2 −1 0 1 2 3 4 Farther right = larger: 3 > 1 (3 is right of 1) −1 > −4 (−1 is right of −4) −9 < −2 (−9 is far left → smaller) 0 > −5 (0 is right of any negative) The sign < or > opens toward the bigger number: −9 < −2 mouth opens at −2
Opposites face across zero
Two numbers that sit the same distance from 0 but on opposite sides — like 3 and −3 — are opposites, formally each other's additive inverse, because they add to zero: 3 + (−3) = 0. Taking the opposite flips a number across zero, swapping its side of the line. We'll come back to this in the guide on opposites and reciprocals.