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## Main Question or Discussion Point

I'm a bit confused on something elementary.

If X is a Hilbert space and A is a subset of X and is uncountable. What exactly does it mean for an element x to be in the span of A? Does it mean x can be expressed as a finite linear combination of elements from A, or can it be infinte and even possibly an uncountble linear combination?

If X is a Hilbert space and A is a subset of X and is uncountable. What exactly does it mean for an element x to be in the span of A? Does it mean x can be expressed as a finite linear combination of elements from A, or can it be infinte and even possibly an uncountble linear combination?