to err is human; admittedly, i'm human.

there are some people that one should never trust. mathematically, i am one of those people, but it has nothing to do with compulsive lying or any sort of malice.

if there were one word to describe me, it's error-prone.

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in today's analysis lecture, i paused during two proofs, suspecting that something didn't look quite right. in one, i miswrote something [1], so my paranoia was fully justified.

in the other, i lost track of whether i had proved the consequence, as advertised in the theorem.

finally i told the students: "all right: let's see if this is a proof or not. this is the consequence we want out of the theorem .." and i wrote it, explicitly in logical symbols.

in the end, there was no gap; we just ended up proving something stronger than we needed, and i was confused with the mismatch of statements.

[sighs] oh well.

in teaching this course, i suppose i'll learn how to be careful on the fly. maybe i've grown lazy, having taught calculus-type courses in all of my experience .. \-:

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on a related note, i wish i could adapt more quickly to this new teaching load: two courses, each with different preps, one of them an upper-level course. all of this week i barely accomplished any research: at best,

1. i found .. ahem .. an error in one of my newer arguments;
2. i came up with an idea to patch it;
3. i suspect now that the idea has another error.

the problem at hand has a natural obstruction; we know it can't be true for some range of exponents (p ≤ n). the idea doesn't (yet?) account for this, so it might "prove" too much.

[sighs again]

[1] it had to do with constructing a subsequence. at first i didn't get the sub-indices right. when i corrected my notation, i immediately realised how awful this would look on a set of student's notes .. \-: