Question on definition of Span

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    Definition Span
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In the context of Hilbert spaces, the term "span" refers specifically to the set of all finite linear combinations of elements from a subset A of the Hilbert space X. An element x is in the span of A if it can be expressed as a finite linear combination of elements from A. Infinite or uncountable linear combinations do not fall within the definition of span in this mathematical framework.

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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 infinite and even possibly an uncountble linear combination?
 
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FINITE linear combination.
 
Thanks. I was thinking that as well but wasn't sure.
 

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