a week ago, i tried to prove one particular fact,

but my argument was too weak. i needed a lemma.

some days ago, i worked out the lemma and obtained a proof.

yesterday i looked at the proof again.

adjusting it carefully, it gives a stronger result.

today i looked at the result. it's too strong.

i think i can find a counter-example ..

.. which means, of course, that the proof is wrong.

i'll let you know if the next proof is "just right."

in other news, today were my first lectures of the fall. i was pleased to find the classrooms easily enough.

you see, a year ago i couldn't remember the room number. so i guessed at random, found a classroom full of calculus students, and summarily began my lecture.

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