Set closure (1 Viewer)

[untouchablecuz]

Is the set S={0,1,2,3,4,5,6,7,8,9} closed under addition? Prove your answer.

my answer:

0+1=1

S
0+2=1

S
8+9=17 is not an element of S

.'. S is not closed under addition

does this count as a proof?

 

[gurmies]

Yep, that's sufficient.

 

[Drongoski]

he only needs to find one example:

That's correct. To show it's not closed under addition, you need only cite 1 example of closure being violated.

 

[Drongoski]

Is the set S={0,1,2,3,4,5,6,7,8,9} closed under addition? Prove your answer.

my answer:

0+1=1

S
0+2=1

S
8+9=17 is not an element of S

.'. S is not closed under addition

does this count as a proof?

You don't need to cite first 2 lines; the 3rd line alone suffices.

 

[Cazic]

No that is not a good proof, what you have dpne is just finding an example which shows the set is not open.

I think you're confusing topology and algebra. His proof is fine, though as Drongoski said the first two lines simply aren't necessary.