Question

Real Number System. How would I write each set using set-builder notation? If you could explain that would be great!
1. {2,4,6,8}
2. {...,-6,-3,0,3,6,...}

Answer 1

What is "set-builder" notation?

Answer 2

A consise way of writing a solution set I.e. {t/t<43} ---> set of all #'s t such that t is less than 43

Answer 3

OK, so what are the first numbers called?

Answer 4

In problem one?

Answer 5

Yes.

Answer 6

2, 4, 6, 8

Answer 7

They are finite set of elements . They r natural numbers, whole numbers, integers and rational numbers

Answer 8

They are also "even" integers, right?

Answer 9

Yes

Answer 10

How would you describe even integers?

Answer 11

Whole number multiples of 2?

Answer 12

Very good. So, an integer that is the product of 2 and any integer.

Answer 13

...-8, -6, -4, -2, 0, 2, 4, 6, 8,...

Answer 14

Okay

Answer 15

So, what is a formula that generates those numbers?

Answer 16

@iamnice101 ?

Answer 17

Sorry I'm here.

Answer 18

Wouldn't the set builder notation for 2,4,6,8 be { x|x=2n+1 , n € N}

Answer 19

They r the set of natural numbers that r even.

Answer 20

Where n belongs to natural numbers

Answer 21

@skullpatrol

Answer 22

@iamnice101 You are looking to build a set using set-builder notation for the finite set of integers, 2,4,6 and 8. You can do this by specifying the dummy variable x and set all the values that this variable is allowed to have. You have specified all natural numbers, with the restriction that n is odd; but you just need a set with only the 4 elements specified \( \{x|x\in(2,4,6,8)\} \).

For part 2, you need all the integers \(\Bbb{Z}\) that are multiples of 3, which includes the negative, positive and zero: \(\{x|x=3n,n\in\Bbb{Z}\}\)

For your reference: http://en.wikipedia.org/wiki/Integer

Please let me know if you have any questions.

Answer 23

Thank u so much

Answer 24

yw