An Elementary Approach to Proving a Continuous Function with All Zero Fourier Coefficients is Identically Zero

When delving into the fascinating world of Fourier series and their convergence properties for functions within the $ C^N $ space, we encounter a fundamental question: Can a continuous function, which

2024-03-02

ARM Mac execute x86 command

Check and switch between ARM and x86 command

2024-01-10

Check Which System is the Python based on

Check whether your python is x86 or arm

2024-01-10

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