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## Main Question or Discussion Point

I've become sort of confused on the topic of the linear span versus spanning sets. I know that the span of a subset is the set containing all linear combinations of vectors in V. Is a spanning set then the same thing, or is it something else?

Also, in terms of bases... A basis is a linearly independent spanning set, but I thought a span was a set containing linear combinations... BUT linear combinations generally indicate linear dependence! If that's the case, how is the spanning set linearly independent? I know I'm missing something here, just not sure what! Anyone have a good description that might help? :shy:

Also, in terms of bases... A basis is a linearly independent spanning set, but I thought a span was a set containing linear combinations... BUT linear combinations generally indicate linear dependence! If that's the case, how is the spanning set linearly independent? I know I'm missing something here, just not sure what! Anyone have a good description that might help? :shy: