`i thought i posted this last week ..`

.. but apparently i didn't, so here it is.

.. but apparently i didn't, so here it is.

on wednesday a student asked me, in the middle of lecture,

"if cαuchy sequences on the real line are the same as convergent ones, then why are there two different notions?"it's a reasonable question.

*why the redundancy?*

i think i gave an excessively blunt answer, though:

without cαuchy sequences,so yes, i stretched the truth a little. there are lots of ways to construct real numbers ..we wouldn't have real numbers.

## 1 comment:

you could always delete a point, say the origin, and now they are not equivalent concepts. show they are not and then discuss how math people love to generalize concepts, etc.

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