# Spivak Calculus Chapter 1 Problem 5 (ii)

Prove : If $$a < b$$ then $$-b < -a$$

My proof :

$$a + (-b) < b + (-b)$$

$$a - b < 0$$

$$a - b + (-a) < 0 + (-a)$$

$$a + (-a) -b < -a$$

$$-b < -a$$

Is my proof correct?

• It looks fine to me. May 25 '20 at 7:36
• well yea it's totally correct May 25 '20 at 8:03

$$a < b$$
$$-a + a - b < -a + b - b$$
$$-b < -a$$