[old post] ask a simple question ..

i thought i posted this last week ..
.. but apparently i didn't, so here it is.

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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 ..