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**[Josh's Notes for Lecture 2](/Lecture_2.pdf)**
#<b>Why the Fourier decomposition is possible?</b>
-**[Josh's Notes for Lecture 2](/Lecture_2.pdf)**
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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 $(0,1) \sim \mathbb R$