My solution for number 1 is not complete. Since $ \oplus_{\mathbf{N}} \mathbf{Q} $ consists of a union of the sets I was looking at, which were n-tuples for a set n, instead of a variable n. Dimberti 14:02, 11 September 2008 (UTC)

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Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett