# For Wednesday, February 26th, 2020

For Wednesday:

• In class Monday we did some existence proofs.  In particular, we considered the definition of convergence of a sequence.  Here it is:
• A sequence $L_1, L_2, L_3, \ldots, L_n, \ldots$ converges to $L$ if, for every $\epsilon$ >0, there exists an $N \in \mathbb{N}$ such that $|L_n - L|$ < $\epsilon$ for all $n$ > $N$.
• Please write the definition above in symbols with universal/existential quantifiers
• Using our discussion in class (that for a “challenge” $\epsilon$, it suffices to take $N = 1/\epsilon$), write a formal proof that the sequence $L_n = 1/n$ converges to 0.
• Watch this Khan Academy video.
• Using the video, write a formal proof that between any two rational numbers, there exists an irrational number.  Be careful:  the video isn’t careful about some details, and it’s just an informal discussion, so to do this right, you have to formalize and fill in some details that are missing.
• With any remaining time, spend quality time with Hammack, Sections 7.3 and 7.4.  There are useful exercises here.
• Note: Sets Badges will be available in class for the last time Friday.  I will then allow you to attempt them as an oral exam in office hour (more details next week).
• An announcement follows for a special event you might be interested in.  Enjoy math?  Maybe your future includes math research as an undergraduate!  There’s also a cool poster.

• Math Research : DemystifiedWhat’s undergraduate math research anyways? Who is it for? It might not be what you think it’s like and it might be for you, even if you haven’t realized it yet! So come to MATH 350 on Wednesday Feb 26 from 5-6 pm to learn more about undergraduate math research, hear about past projects done by students at CU and learn more about the opportunities for math research experiences available to the undergraduate students on campus. There will also be be free soft drinks and pizza. Everyone is welcome!
• When: Wednesday Feb 26 from 5-6 pm

Where: MATH 350 (Mathematics Building)

Who: Organized by the Math Club and Diversity Committee