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Countable Sets and Limit of Sequence of Functions

Show that there is a countable set F of functions of form

x--->a_0 + a_1cosx + a_2cos(2x) + ... +a_ncos(nx)

such that every continuous real-valued function on [0,pi] is the uniform limit of a sequence of functions (f_n) in F.

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Countable Sets and Limit of Sequence of Functions are investigated.

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