1) Which of the following sets are equal?

a) {1, 2, 3}

b) {3, 2, 1, 3}

c) {3, 1, 2, 3}

d) {1, 2, 2, 3}

Is this as simple as saying b and c are equal because they contain the same numbers? Or is it more complicated than that?

Printable View

- Mar 25th 2013, 03:36 PMrhyminSet Theory Question
1) Which of the following sets are equal?

a) {1, 2, 3}

b) {3, 2, 1, 3}

c) {3, 1, 2, 3}

d) {1, 2, 2, 3}

Is this as simple as saying b and c are equal because they contain the same numbers? Or is it more complicated than that? - Mar 25th 2013, 03:41 PMProve ItRe: Set Theory Question
Yes that is correct.

- Mar 25th 2013, 03:42 PMrhyminRe: Set Theory Question
Is there anyway to show work for this problem? Or is just saying "b and c are equal because they contain the same set of numbers" enough?

- Mar 25th 2013, 03:43 PMrhyminRe: Set Theory Question
Hmm, my friend just told me that they are equal if every element of one is a subset of the other and that they are all equal.

Now I'm more confused lol. - Mar 25th 2013, 03:44 PMProve ItRe: Set Theory Question
Two sets are equal if they contain exactly the same elements and nothing else. It's as simple as that...

- Mar 25th 2013, 03:44 PMPlatoRe: Set Theory Question
- Mar 25th 2013, 03:51 PMHallsofIvyRe: Set Theory Question
Plato's point is that a

**set**does not have the same object multiple times. However, some texts would simply ignore the multiple occurances and say that**all**those sets are the same- and would be better written as just {1, 2, 3}. - Mar 25th 2013, 03:56 PMrhyminRe: Set Theory Question
Hmm, I'm confused again...sorry for my ignorance. :(

- Mar 25th 2013, 03:57 PMrhyminRe: Set Theory Question
Oh, so they are all the same really? Since duplicates don't matter?

- Mar 25th 2013, 04:04 PMPlatoRe: Set Theory Question
- Mar 25th 2013, 04:07 PMrhyminRe: Set Theory Question
Yes, thank you!

- Mar 26th 2013, 03:02 AMDrSteveRe: Set Theory Question
All 4 are different ways of writing the same set. The most natural way to write this set is {1,2,3}.