Hello,

I need help with the following problem:

Prove that Card(l^p) = c (cardinality of the continuum), p >= 1.

I am not quite sure how to start the proof. I'd appreciate anyone's help. Thank you.

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- September 21st 2010, 04:42 PManlysCardinality of the continuum
Hello,

I need help with the following problem:

Prove that Card(l^p) = c (cardinality of the continuum), p >= 1.

I am not quite sure how to start the proof. I'd appreciate anyone's help. Thank you. - September 21st 2010, 05:28 PMDontKnoMaffunable to understand
I would like to help you but I am unsure what your notation means. You are trying to prove that the cardinality of some set I to the pth power is equal to c? I am sorry if this is a dumb question, this is my first post onto this website.

- September 21st 2010, 05:40 PManlys
Hi, that's okay. Actually, that is not an I, it's a lower case for L. The notation l^p refers to the metric space with || x ||_p = (summation |x_i|^p from i = 1 to infinity)^(1/p). That's all I was given in the problem.

- September 22nd 2010, 01:10 AMTikoloshe
I think the additional structure on is a red herring. All you need is that , and that .

Then, .