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July 18th, 2017, 02:20 AM   #1
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Should span be a finite linear combination only?

Wiki says infinite linear combination should be excluded off of the definition of span. So should we answer "Yes" to the following question appearing in UC Davis notes?:

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July 18th, 2017, 02:30 AM   #2
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The answer is indeed yes.
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August 17th, 2017, 04:35 PM   #3
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Note that in "functional analysis", where we have infinite dimensional vector spaces and a notion of limits, so that we can add an infinite number of vectors, we can have a "span" of an infinite number of vectors. Fourier series are an example of that.
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