Tuesday, April 12, 2011

[old post] ask a simple question ..

i thought i posted this last week ..
.. 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, we wouldn't have real numbers.
so yes, i stretched the truth a little. there are lots of ways to construct real numbers ..

1 comment:

Anonymous said...

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.