Would the cardinality of a set S = {a, b, {c, d}} be 5?

[Gear300]

Would the cardinality of a set S = {a, b, {c, d}} be 5?

 

[some_dude]

Would the cardinality of a set S = {a, b, {c, d}} be 5?

No, 3. The elements of the set are a, b, and {c,d}.

 

[Gear300]

No, 3. The elements of the set are a, b, and {c,d}.

But let us say that H = {c,d}. Then S = {a, b, H}. Shouldn't it be so that if H ⊂ S, c ϵ H, and d ϵ H, then c ϵ S and d ϵ S...which would mean that you could pull out more than 3 elements out of S (unless it is improper to associate elements of a particular element of a set to that set).

 

[chingkui]

H ϵ S, not H ⊂ S

 

[Gear300]

I see...Thanks for the replies.