Some Comparing lemmas in analysis (epsilon delta language) lemma of "less than" Content: \(x, y \in \Bbb{R}\), \(\forall \epsilon \gt 0\), \(x \lt y + \epsilon\), then \(x \leq y\) Proof lemma of "Equal" Content: \(x, y \in \Bbb{R}\), \(\forall \epsilon \gt 2023-12-18 Daily Logs > Math > Analysis #Math #Analysis #Real Analysis #Metric #Functional Space
A Fun Limit: relationship between (n!)^(1/n) and n Relationship between $(n!)^{\frac{1}{n}} and n$ 2023-12-18 Daily Logs > Math > Analysis #Math #Analysis #Real Analysis #Limit #Order of infinity
Relationship between Ratio and Root test Relationship between Ratio and Root test 2023-12-18 Daily Logs > Math > Analysis #Math #Analysis #Real Analysis #Limit #Order of infinity #Ratio Test #Root Test
convergence of sum of sin(aknx)/n Talk about the convergence of the sum of $\sum_{n=1}^{\infinity} \frac{sin(anx)}{x}$ 2023-12-17 Daily Logs > Math > Analysis #Math #Analysis #Real Analysis #Limit #Order of infinity #Convergence of Sum
x > sinx: Three ways of proving More information can be found here: A Chinese Platform: How to prove \(sin(x) < x\) regiously? Math.stackexchange: Sine inequality: How to prove that \(|sin(𝑥)|≤|𝑥|\) 2023-12-15 Daily Logs > Math > Analysis #Math
Metric in L^p Metric in L^p This is a note for proof of \[ \left[ \int _{a}^{b}\left| f\left( x\right) \right| ^{p}dx\right]^{\frac{1}{p}} \] is a norm of \(L^p\) space. Here is the structure of the whole proof (se 2023-11-24 Daily Logs > Math > Analysis #Math #Analysis #Real Analysis #Metric #Functional Space
Rudin Analysis Exercise 2.23 Explained proof of an exercise question 2023-10-31 Daily Logs > Learning Logs > Math > Analysis #Math #Analysis #Real Analysis #Rudin #Countablility
Operator Precedence in C Bug of operator precedence in C 2023-10-26 Daily Logs > Learning Logs > C #Learning Log #C #operator #debug