Answer to Question #278161 in Calculus for Ali

Question

Given that R denotes the set of all real numbers Z, the set of all integers, and Z set of all negative integers, describe each of the following:

Answer 1

QUESTION:

Given that $\R$ denotes the set of all real numbers, $\Z$ , the set of all integers, and $\Z^+$ the set of all positive integers and $\Z^-$ the set of all negative integers, describe each of the following sets.

a. {X$\in \R$ | -5<x<1}

b. {X$\in \Z$| -5<x<1}

c. {X$\in \Z^+$ |-5<x<1}

d. {X$\in \Z^-$ | -5<x<1}

SOLUTION

(a)

$\begin{Bmatrix} X\in\R | -5<x<1 \end{Bmatrix}$

All real number in the interval

$[-5,1 ]$

There are infinite elements

(b)

$\begin{Bmatrix} X\in\Z|-5<x<1 \end{Bmatrix}$

All real numbers between

$-5$ and $1$

The elements are

$-4,-3,-2,-1,0$

(c)

$\begin{Bmatrix} X\in\Z^+|-5<x<1 \end{Bmatrix}$

There are no elements

$\begin{Bmatrix} \empty \end{Bmatrix}$

(d)

$\begin{Bmatrix} X\in\Z^-|-5<x<1 \end{Bmatrix}$

All negative integers between $-5$ and $1$

There are four elements

$-4,-3,-2,-1$