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| -rw-r--r-- | Fourier Series.page | 10 |
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diff --git a/Fourier Series.page b/Fourier Series.page index 251c509..79bd095 100644 --- a/Fourier Series.page +++ b/Fourier Series.page @@ -1,12 +1,12 @@ #<b>Why the Fourier decomposition is possible?</b> -We first begin with a few basic identities on the size of sets. Then, we will show that the set of possible functions representing sets is not larger than the set of available functions. This at best indicates that the Fourier series is not altogether impossible. - +We first begin with a few basic identities on the size of sets. Then, we will show that the set of possible functions representing sets is not larger than the set of available functions. This at best indicates that the Fourier series is not altogether impossible. + ## To show that $(0,1) \sim \mathbb R$ ---> could someone fill this out? +--> could someone fill this out? ## Cantor's proof for $\mathbb R > \mathbb N$ ---> don't have the notes for this +--> don't have the notes for this ## Proof that no. of available functions is greater than number of functions required to define the periodic function ---> don't have the notes for this +--> don't have the notes for this #<b>Why Fourier decomposition is plausible?</b> To show that Fourier series is plausible, let us consider some arbitrary trignometric functions and see if it is possible to express them as the sum of sines and cosines: |