list the elements in sets.

• Apr 16th 2010, 10:03 AM
jvignacio
list the elements in sets.
hey guys having problems with this question.

List the elements in the following sets:

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

Elements x = 1,2,3,4

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

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

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

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

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

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

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

5. $\{ \}$

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

Any help with these 5 questions would be much appreciated.
• Apr 16th 2010, 10:17 AM
Quote:

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

List the elements in the following sets:

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

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

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

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

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

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

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

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

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

5. $\{ \}$

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

Any help with these 5 questions would be much appreciated.

.
• Apr 16th 2010, 10:25 AM
jvignacio
Quote:

.

thanks for the help Archie! understood :)
• Apr 16th 2010, 10:52 AM
Plato
Quote:

Originally Posted by jvignacio
thanks for the help Archie! understood

One comment: some textbooks include 0 in $\mathbb{N}$, but others do not.
So check your textbook to see which definition it uses.
• Apr 16th 2010, 10:54 AM
jvignacio
Quote:

Originally Posted by Plato
One comment: some textbooks include 0 in $\mathbb{N}$, 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!