Freshman intended math+cs major.
Welcome to discuss 104 problems or other math/cs with me ^^ happy to learn from everyone!!
Courses I have taken:
math W128A
math 53
math 54
cs 61A
Current Course:
math 104
math 113
math 110
cs 70

Peano axiom for $\mathbb{N}$ produce axiomic instead of constructive definition, but how can we know that the $\mathbb{N}$ that satisfies all the axioms is unique?
Is it that we use these axioms to define a group of sets that can be considered “natural numbers”, and then use induction to show that A and B that satisfies all axioms must be equal? (since we already have inductive property for both A and B now)
I finally understood how to upload Ross 3.2 to this site now..

Real number has two defs, but textbook did not show the equivalence and their equivalence to completeness… HW is here

HW for sequence and limits I did not finish 10.11 I found an inf for the sequence to be 1/2 but I can no longer proceed further…

Got a hint from a textbook to evaluate $\int_0^{\frac{\pi}{2}}\sin^{2n+1}x dx$ first, now it worked but literally dont understand how we are supposed to think about this at the first place :(

Subsequential limits are difficult for me.

During class there are 2 that I did not follow at first:

1: there is a subsequence approaching $limsup(s_n)$ monotonically.

2: the set of subsequential limit of a bounded sequence is closed (This one is better explained just by a graph)

HW3 is quite easy this week though, but cantor diagonal is a really amazing technique.

Series is no good for me.

I spent my whole life on the last question in rudin in this week HW4.

Here are my 5 questions:

In our proof, divergence in quotient and root test both implies an almost-geometric sequence in the tail. I really dont understand how is it helpful in determining most of the non-obvious diverging series, since we usually dont need to spend much effort to show an increasing sequence diverge. :(

In hw I see for a positive sequence, the fact that its partial sum is a monotone sequence can be helpful to see its convergence. Is there a lot of instances that we can try to “zip” a sequence into positive parts, and then try to bound the partial sum? (its really just an intuition that may not be useful at all)

When we try to show some convergence and divergence of some series expressed as fractions (i.e. $\frac{n+1}{n^3+1}$) can we just compare the power terms and say it is convergent? (since 1/n^2 is) or this only works for sequence.