Hello! My name is Aaron Zaks, I'm a pure math major. I transferred to Berkeley this year, so I'm a third year, but this is my first year studying here. Excited to take 104!

HW4 Questions:

1. What does it mean to “realize” limsup as sup by supS = limsup + ε?

2. Why does the ratio test only require that limsup < 1, not that the ratio converges?

3. Is there a simpler technique for proving lim(an bn) = lim(an) lim(bn)? specifically with the inequalities, I found those confusing

4. Do we ever have to apply the Dedekind cut in our proofs? Or was that just a construction to get us started with the reals?

5. I understand that the rationals are countable, but what order is their enumeration? Does it matter?

Homework:

[hw1math104_-_aaron_zaks.pdf