Question

If N = {all real numbers} and subset S = {multiples of 4 less than zero}, what is S′?

Answer 1

What does the ' mean in this notation?

Also, \(\mathbb{R}\) is used for all reals. Also,
\[S:=\{4k: 4k<0 \wedge k \in \mathbb{Z}\}\]

Answer 2

\[\mathbb{N}\] is usually reserved for natural numbers
\[\{1,2,3,...\}\] just thought i would mention it

Answer 3

actually the more i look, the more the problem is confusing me

Answer 4

Is it one of these {multiples of 4 greater than zero}

{even numbers less than zero}

{odd numbers less than zero}

{all real numbers excluding multiples of 4 less than zero}

Answer 5

if we are living in the universe of real numbers, all can be written as multiples of 4

Answer 6

Disregard my definition for \(S\).

Answer 7

@Limitless am i being silly here?
if the universe is \(\mathbb{R}\) does it make sense to talk about multiples of 4??

Answer 8

I don't understand what \(S'\) means. @satellite73, I think you are correct about that. But, I do not see that as relevant because I don't know what's being asked.

Answer 9

@CallMeKelly your teacher wants the last one as an answer

Answer 10

this one
"{all real numbers excluding multiples of 4 less than zero}
"

Answer 11

Is \(S'\) the elements not in \(S\)?

Answer 12

i suppose i should leave my critique to myself so as not to confuse, but i cant help remarking that this is a really poor question on several levels

Answer 13

S' is the complement of S

Answer 14

@Zarkon am i being stupid here?

Answer 15

no matter what the universal set is I take multiples of a natural number to be any integer times that number

Answer 16

ok
in any case the answer wanted is the last one

Answer 17

yes

Answer 18

then my only objection is "let N be all real numbers" but whatever, i guess you can use any letter you like

Answer 19

I object to that too...will lead to confusion down the road.

Answer 20

This question doesn't seem well-motivated. If they're going to teach complements, why not use more important sets than just some arbitrarily defined set?

Answer 21

whenever I teach this stuff I always start with simple finite sets

Answer 22

I can understand that. I guess it really depends on your audience. Different people prefer different approaches to the same thing.

Answer 23

i am still somewhat baffled by multiples of 4 in \(\mathbb{R}\) what is wrong with
"integer multiples of 4"?

Answer 24

that would be better wording