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: