Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Absolute Value Definition

If P and Q are two points on a real number line with coordinates a and b, respectively, the distance between P and Q, denoted by d(P, Q) is d(P, Q) = |b - a|

We can say that | a - b | = | b - a | since it follows that d(P, Q) = d(Q, P).

Why does the order of a and b inside the absolute value bars does not matter?

For example, why does | 4 - 5 | = | 5 - 4 |?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,637

Re: Absolute Value Definition

Absolute value means if a number is negative you replace it by the same magnitude but positive.  If the number is already positive (or zero) then do nothing to it.

So |5-4| = |1| = 1 and |4-5| = |-1| = 1 as well.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Absolute Value Definition

Absolute value means if a number is negative you replace it by the same magnitude but positive.  If the number is already positive (or zero) then do nothing to it.

So |5-4| = |1| = 1 and |4-5| = |-1| = 1 as well.

Bob

Isn't this much better than Section 3.6?