Sets and Double Sum Questions...

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.

http://pearcy.homeftp.org/summation.jpg

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

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

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Yes, AFAIK.

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Does {3} = {{3}}?

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

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Does 0 belong to the empty set?

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Possibly No, but I am not sure.

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Does 0 belong to the empty set inside a set?

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

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Originally Posted by demon8991

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?

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No

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Originally Posted by demon8991

Does 0 belong to the empty set inside a set?

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No

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Originally Posted by 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

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This will help

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Originally Posted by Glaysher

This will help

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

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Originally Posted by Glaysher

This will help

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

S = N(N + 1)²/2

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Originally Posted by krtxmrtz

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

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