(Sheet 5) Starter - Bolzano-Weierstrass Theorem
Bolzano-Weierstrass Theorem Let \( (a_n) \) be a bounded real sequence. Then \( (a_n) \) has a convergent subsequence.
Below are jumbled statements. Your challenge is to sort them into two separate proofs of this theorem. When you've done that, how do the two proofs compare? Do you have a favourite?
(There are some different legitimate orderings of the statements, but unfortunately I can't figure out a convenient way to record this so that Moodle will check for you. In particular, if you have the two proofs in the opposite order from Moodle then it will tell you you're incorrect, when of course you might not be. To avoid this issue, I'll tell you that N comes first in my ordering. There are still some options for correct orderings within each proof, so if you're confident that your argument works then please don't be put off by Moodle.)
Grading method: Last attempt