Sets and Double Sum Questions...

[demon8991]

Just trying to get my head round some maths notation some of it is ok but some im stuggling with.

Is {3} a sub set of {3}?

Does {3} = {{3}}?

Does 0 belong to the empty set?

Does 0 belong to the empty set inside a set?

Im also struggling with this double sum question, as im trying to teach myself this subject.

[krtxmrtz]

Hi, welcome to the forums.

I can give you a bit of a push with the double sum. See the attached figure. Unfortunately I just don't know how to calculate the sum of the i²'s

[Harsh Gupta]

Is {3} a sub set of {3}?

Yes, AFAIK.

Does {3} = {{3}}?

No, {3} is an element of {{3}}.

Does 0 belong to the empty set?

Possibly No, but I am not sure.

Does 0 belong to the empty set inside a set?

This depends largely on the previous answer. So, my answer would be no. But again, I am not sure on this one too.

[Glaysher]

Just trying to get my head round some maths notation some of it is ok but some im stuggling with.



Does 0 belong to the empty set?

No

Does 0 belong to the empty set inside a set?

No

[Glaysher]

Hi, welcome to the forums.

I can give you a bit of a push with the double sum. See the attached figure. Unfortunately I just don't know how to calculate the sum of the i²'s

This will help

[krtxmrtz]

This will help

I can't remember, was there some standard technique for this type of sums?

[krtxmrtz]

This will help

Using Glaysher's result, the sum of post #2 becomes

S = N(N + 1)²/2

[Glaysher]

I can't remember, was there some standard technique for this type of sums?

There are several ways to prove it but it is considered a standard result usually given in formula books.