 # Author: Chiu Yau

• ## Maths – Differentiation (1)

Before start, limit of $$f$$ when x-> $$c$$ $$\neq f(c)$$ $$f(x) = \frac{x^{2}-1}{x-1}$$ is defined everywhere except x=1 $$f(1)$$ ? $$f$$ is not defined at $$x=1$$ When x close to 1, $$x$$ -> $$1$$ f(x) close to 2, >>> $$f(x)$$ -> $$2$$ $$\neq f(1) = 2$$…

• ## Introduction to Linear Algebra and Calculus III – Mathematical Induction

Such a mathematical process of deducing the general result is called induction. However, the validity of the above identity is questionable since it has not been tested for all positive integers. To resolve such a difficulty, a mathematical procedure known as Mathematical Induction (M.I.) is introduced.  Example 1. Base Step: Show P(1) is true P(n):…

• ## Introduction to Linear Algebra and Calculus II – Exponential Function: The Number e

sister function of exponential function $$log_e = ln$$ e.g.: $$y=log_3 81$$ $$3y=81$$ $$y=4$$ Log func() = find the power of the func() raise the power of the base, $$\sqrt{3}$$ to equal $$x$$ (i.e., 9 on above). Related tutorials:

• ## Introduction to Linear Algebra and Calculus I

Introduction to Linear Algebra and Calculus I By Chiu Yau

• ## Discreet Maths – Set Operations

https://math.stackexchange.com/questions/2196858/what-does-a-transitive-set-exactly-imply Set Relations: Reflexive E.g.1 { (1,1),(2,2),(3,3),(4,4) } E.g.2 { (3,3),(4,4),(5,5) } Everybody talks to itself. *Reflexive is always transitive Symmetric E.g.1 { (1,2),(2,1) } , if (1,2) then (2,1) must exist. E.g.2 { (1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3) } For (1,2,3) multiple (1,2,3): Transitive As (a,b) ∈ R and (b,c) ∈ R , then (a,c) ∈ R.

• ## Motherboard Form Factor

Tabular information Form factor Originated Date Max. size[info 1]width × depth Notes(typical usage, Market adoption, etc.) XT IBM 1983 216 × 279 mm(8.5 × 11 in) Obsolete, see Industry Standard Architecture. The IBM Personal Computer XT was the successor to the original IBM PC, its first home computer. As the specifications were open, many clone motherboards were produced and it became a de facto standard. AT (Advanced Technology) IBM 1984…

• ## Quick Tip: How to Permanently Change SQL Mode in MySQL

Disclaimer: This is a copy of Quick Tip: How to Permanently Change SQL Mode in MySQL – SitePoint  was working on a legacy project recently and needed to import some data from MySQL 5.5. All the queries in the code worked perfectly in MySQL 5.5, so I assumed an upgrade to 5.7 would be seamless.…

• ## How to install Coturn (TURN / STUN Server) in Ubuntu 22.04 via PPA | UbuntuHandbook

Disclaimer: This is a copy of How to install Coturn (TURN / STUN Server) in Ubuntu 22.04 via PPA | UbuntuHandbook Ubuntu 22.04 misses coturn TURN and STUN server package in its system repository. Here’s how to install it via PPA. Coturn is a free open source implementation of TURN and STUN Server, which can…

• ## Cloudflare Allowed Ports with Proxy Enabled

Disclaimer: This is an copy of Network ports · Cloudflare Fundamentals docs Network ports Learn which network ports Cloudflare proxies by default and how to enable Cloudflare’s proxy for additional ports. ​​Network ports compatible with Cloudflare’s proxy By default, Cloudflare proxies traffic destined for the HTTP/HTTPS ports listed below.HTTP ports supported by Cloudflare 80 8080…