# Thread: list the elements in sets.

1. ## list the elements in sets.

hey guys having problems with this question.

List the elements in the following sets:

1. $\displaystyle \{ x \epsilon \mathbb{N} : x^2 < 23\}$

Elements x = 1,2,3,4

2. $\displaystyle \{ x \epsilon \mathbb{Z} : x^2 < 23\}$

Elements x = -4,-3,-2,0,1,2,3,4

3. $\displaystyle \{ x \epsilon \mathbb{R} : x^3 + 5x\}$

$\displaystyle \Rightarrow x^3 + 5x = 0$
$\displaystyle \Rightarrow x(x^2 + 5) = 0$

so I know $\displaystyle x = 0$, but dont know how to find $\displaystyle x$ from $\displaystyle x^2 + 5 = 0$

4. $\displaystyle \{ x \epsilon \mathbb{Q} : x^2 + 4 = 7\}$

I know Q is rational numbers but dont know how to find this one.

5. $\displaystyle \{ \}$

This is just an empty set so would it be elements:
$\displaystyle \emptyset$ ?

Any help with these 5 questions would be much appreciated.

2. Originally Posted by jvignacio
hey guys having problems with this question.

List the elements in the following sets:

1. $\displaystyle \{ x \epsilon \mathbb{N} : x^2 < 23\}$

Elements x = 1,2,3,4 what about 0 ?

2. $\displaystyle \{ x \epsilon \mathbb{Z} : x^2 < 23\}$

Elements x = -4,-3,-2,0,1,2,3,4

3. $\displaystyle \{ x \epsilon \mathbb{R} : x^3 + 5x\}$ $\displaystyle \color{blue}x^3+5x=0\ ?$

$\displaystyle \Rightarrow x^3 + 5x = 0$
$\displaystyle \Rightarrow x(x^2 + 5) = 0$ $\displaystyle \color{blue}x^2=-5$ is not real, x=0 is the only solution

so I know $\displaystyle x = 0$, but dont know how to find $\displaystyle x$ from $\displaystyle x^2 + 5 = 0$

4. $\displaystyle \{ x \epsilon \mathbb{Q} : x^2 + 4 = 7\}$ $\displaystyle \color{blue} x^2=7-4=3,\ x=\sqrt{3}\ is\ not\ rational,\ no\ solution$

I know Q is rational numbers but dont know how to find this one.

5. $\displaystyle \{ \}$

This is just an empty set so would it be elements:
$\displaystyle \emptyset$ ?

Any help with these 5 questions would be much appreciated.
.

3. Originally Posted by Archie Meade
.
thanks for the help Archie! understood

4. Originally Posted by jvignacio
thanks for the help Archie! understood
One comment: some textbooks include 0 in $\displaystyle \mathbb{N}$, but others do not.
So check your textbook to see which definition it uses.

5. Originally Posted by Plato
One comment: some textbooks include 0 in $\displaystyle \mathbb{N}$, but others do not.
So check your textbook to see which definition it uses.
Yeah our lecturers include 0 as a natural, just forgot to put it thanks for the comment and reminder!