Q1. Find a counterexample to the sta... [FREE SOLUTION]

Chapter 2: Q1. (page 92)

Find a counterexample to the statement to find the greatest integer function of xwhen xis not an integer, round xto the nearest integer.

Short Answer

Expert verified

The counter example for the given statement is $[[2.6]] = 2$

Step by step solution

Step-1 – Greatest integer function

The Greatest integer function, written $f (x) = [[x]]$ is an example of step function. The symbol $[[x]]$ means the greatest integer less than or equal to x

Step-2 – Suitable function for given statement.

The given statement is to find the greatest integer function of x when x is not an integer, round x to the nearest integer.

Suitable function for this case is $g (x) = [[x]]$

$\begin{array}{l} L e t 鈥� u s 鈥� c o n s i d e r 鈥� x = 2.6 \\ g (x) = 銆� x 銆� \\ g (2.6) = 銆� 2.6 銆� \\ = 2 \end{array}$

Step-3 – Determine the difference.

Original function was:

$\begin{array}{l} x = 2.6 \\ 2 < 2.6 < 3 \end{array}$

Here, we can observe that to find the greatest integer function of x when x is not an integer, we didn鈥檛 round x to the nearest integer. We round to integer less than x.

So, the counter example for the given statement is $[[2.6]] = 2$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Find a counterexample to the statement to find the greatest integer function of xwhen xis not an integer, round xto the nearest integer.

Short Answer

Step by step solution

Step-1 – Greatest integer function

Step-2 – Suitable function for given statement.

Step-3 – Determine the difference.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Geometry

Decision Maths

Applied Mathematics

Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.