O'Reilly logo

Discrete Mathematics and Combinatorics by T. Sengadir

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

2.7 SOME BASIC FUNCTIONS AND THEIR PROPERTIES

What do we mean when we say that 3.14 is an approximation of π ? This means that on the real line these two numbers are ‘close’ to each other. The numbers −7.1 and −7 are closer to each other than the pair 10 and −1000. The modulus function is useful to measure the distance between two numbers. |x| is just the distance between origin and the point x. We formally define the modulus function || : ℝ → ℝ+ as follows.

2.7.1 The Modulus Function

 

|x| = x, x ≥ 0     (2.11)

 

       = −x, x   < 0.        (2.12)

 

The distance between two points x and y is nothing but |xy|. The statement |x| ≤ a is equivalent to the statement −axx.

PRACTICE 2.31

Show that the function f : ℝ → ℝ defined as f(x

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required