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| author | siveshs <siveshs@gmail.com> | 2010-07-03 05:05:44 +0000 |
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| committer | bnewbold <bnewbold@adelie.robocracy.org> | 2010-07-03 05:05:44 +0000 |
| commit | d36ea22536d73605f1c262ecd3f74966198cdd16 (patch) | |
| tree | aaff0d3c705f083363a57543cb9fce9eb6b3b6e2 /Fourier Series.page | |
| parent | c38516e060b53321aabfc5a011c5a52a489c66ce (diff) | |
| download | afterklein-wiki-d36ea22536d73605f1c262ecd3f74966198cdd16.tar.gz afterklein-wiki-d36ea22536d73605f1c262ecd3f74966198cdd16.zip | |
final editing
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| -rw-r--r-- | Fourier Series.page | 6 |
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diff --git a/Fourier Series.page b/Fourier Series.page index 0de4c38..cfea31b 100644 --- a/Fourier Series.page +++ b/Fourier Series.page @@ -1,5 +1,9 @@ #<b>Why Fourier series possible?</b> -We first begin with a few basic identities on the size of sets. Show that the set of possible functions representing sets is not larger than the set of available functions? +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 $(0,1) \sim \mathbb R$ +## Cantor's proof for $\mathbb R > \mathbb N$ +## Proof that no. of available functions is greater than number of functions required to define the periodic function #<b>Why Fourier series 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: |