Open thread, Oct. 5 - Oct. 11, 2015

MrMind

If it's worth saying, but not worth its own post (even in Discussion), then it goes here.

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If it's worth saying, but not worth its own post (even in Discussion), then it goes here.

Notes for future OT posters:

1. Please add the 'open_thread' tag.

2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)

3. Open Threads should be posted in Discussion, and not Main.

4. Open Threads should start on Monday, and end on Sunday.

I think it's actually cleaner to prove the theorem non-inductively (though I appreciate that what GS asked for was specifically a cleaned-up inductive proof). E.g.: "Count pairs (vertex,edge) where the edge is incident on the vertex. The number of such pairs for a given vertex equals its degree, so the sum equals the sum of the degrees. The number of such pairs for a given edge equals 2, so the sum equals twice the number of edges."

(More visually: draw the graph. Now erase all of each edge apart from a little bit at each end. The resulting picture is a collection of stars, one per vertex. How many points have the stars in total?)