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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

WebSocket on stock data with latency issue

WebSocket Latency issues with REAL WORLD SITUATION & SOLUTION
2023-10-17
Daily Logs > Learning Logs
#Learning Log #WebSocket

WebSocket Introduction

Introduction on concept of WebSocket
2023-10-17
Daily Logs > Learning Logs
#Learning Log #WebSocket
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