The 3 dimensional space that we inhabit must have a basis of 3 vectors which is fair enough.(adsbygoogle = window.adsbygoogle || []).push({});

But in my partial differential equations class in which fourier series was introduced, it was said that piecewise smooth function space has a basis of an infinite number of vectors. If there is a simple enough answer to this, I am curious to why this is. Does it have to do with the discontinuities that can arise in PWS space?

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# Vector Space Question

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