User:Techit/Knowledge dump

Hello, welcome to Techit's knowledge dump page. Here I will dump as many knowledge as possible for collection in the future use.

Mathematics

Mathematics is the study field I hated the most, even though I chose to study in Sci-Math program. Anyways just let's get into the point.

Set

Imagine a data array, it's a set. Set is a collection of different stuff. For example A = $A=\{1,2,3,4,5,6,7,8,9\}$ or $\text{Slave}=\{\text{Diskette},\text{GameCreator}\}$.

Elements / Members

A stuff in a data set is called "element" or "member", so to write a set notation we use $\in$(in). So let's see some examples below.

1. $A=\{x|x\in {𝕀}^{+},-5<x\le 12\}$
2. $B=\{x|x\in \mathbb{P},-5\le x\le 23\}$

To translate set notation to normal human-being data set we look at $\in$then use our brain to analyze, after that A should be {x which x in $I^{+}$ (positive integer), x greater than -5 but less or equals to 12}, which in conclusion to be $A=\{1,2,3,4,5,6,7,8,9,10,11,12\}$.

Additional info: you might see these stupid blackboard letters e.g. $ℝ,\mathbb{Q},𝕀,\mathbb{P}$, these can be denotes to...

• $ℝ$ = real numbers
• ${ℝ}^{+}$ = positive real numbers
• ${ℝ}^{-}$ = negative real numbers
• $\mathbb{Q}$ = rational numbers
• ${\mathbb{Q}}^{+}$ = positive rational numbers
• ${\mathbb{Q}}^{-}$ = negative rational numbers
• $𝕀$ = integer numbers
• ${𝕀}^{+}$ = positive integer numbers
• ${𝕀}^{-}$ = negative integer numbers
• $\mathbb{N}$ = natural numbers
• $\mathbb{P}$ = prime numbers

Venn diagram

Venn diagram is a way to draw set, usually to visualize set operations (usually union, intersection and complement) however it's a pain in ass to draw so I will not talk much about this thing. But for now let's get to know "universe" ($𝕌$; can be written as U, U, 𝓤, Ｕ or whatever the hell you would like) or data range or whatever the heck it's called but in Thai it's called เอกภพสัมพัทธ์.

Subset

Subset is what I hated the most in this topic so let's get fast. So you have $A=\{1,2,3\}$ the A's subset would be $\{\},\{1\},\{2\},\{3\},\{1,2\},\{1,3\},\{2,3\},\{1,2,3\}$, if you don't see the pattern, this is the pattern $\{\},\dots ,A$ where $\dots$ is combination of every member from 1 member {1} to 2 {1,2} to 3 {1,2,3} members to $\text{n}$ members. The total subset amount will be $n(A)*2$. In this example $n(A)$ is 3 so we will have a total subset of 6.

Here's what you might need to know more about subset;

1. {} is called "empty set" or "null" in computer nerd language
2. $\text{Ø}$ can be used to represent empty set too
3. $A\subseteq B⟺\mathrm{\forall }x(x\in A\Rightarrow x\in B)$ - A is a subset of B if every element of A is also an element of B
4. $A\subset B⟺(A\subseteq B,A\ne B)$ - A is a proper subset only if A is subset of B and A is not equals to B

Power set

Power set is related to subset; it's just a set of all subset in that set. Let's bring $A=\{1,2,3\}$ guess what is $P(A)$? Yes. $P(A)=\{\text{Ø},\{1\},\{2\},\{3\},\{1,2\},\{1,3\},\{2,3\},\{1,2,3\}\}$

Basic set operations

Intersection

The intersection of two sets $A$⁠⁠ and $B$ ⁠⁠ is a set denoted ⁠⁠$A\cap B$ whose elements are those elements that belong to both $A$⁠⁠ and ⁠⁠$B$. That is,$A\cap B=\{x|x\in A\wedge x\in B\},$ where $\wedge$ denotes logical and.

Union

The union of two sets $A$⁠⁠ and $B$ is a set of elements which are in $A$, in $B$, or in the both $A$ and $B$.

Imagine $A=\{1,3,5,7,9,10\}$ and $B=\{2,4,5,6,8,10\}$ then $A\cup B=\{1,2,3,4,5,6,7,8,9,10\}$

Complement

The complement of $A$ is to everything but $A$.

Imagine $𝕌=\{1,2,\dots ,9\}$ and $A=\{1,3,5,7\}$ and $B=\{2,4,5,6\}$ then $A^{\prime }=\{2,4,6,8,9\}$.

Physics

This field of study happen to be exist because an apple fell onto Isaac's head.

Scientific notation

This is nothing much, just some number shorteners.

Conversion

This is very important, you need to know. Say you want to convert $3.56*10^{15}ng$ (nano gram) to $kg$ (kilo gram); what you need to do is you convert to the $ng$ to $g$ first. Take a look at the SI prefixes table below, multiply $3.56*10^{15}$ with the exponent of that converting prefix; "nano" here. $3.56*10^{15}*10^{-9}$, boom you got $3.56*10^{6}g$. Next convert $g$ to $kg$ by dividing $3.56*10^{6}g$ by $10^3$ (kilo), you got $\frac{3.56*10^6}{10^3}$. Then you must invert the $10^3$ to $10^{-3}$ and from dividing to multiplying so you got $3.56*10^6*10^{-3}$, and the final answer will be $3.56*10^{3}kg$.

Metric prefix

We use this to write instead of long numbers e.g. $1,000,000\text{bytes}=1*10^6\text{bytes}=1\text{mega bytes}$. We use International System of Units

SI prefixes

Prefix	Initial	Decimal	Exponent Form
Exa	E	1,000,000,000,000,000,000	$10^{18}$
Peta	P	1,000,000,000,000,000	$10^{15}$
Tera	T	1,000,000,000,000	$10^{12}$
Giga	G	1,000,000,000	$10^9$
Mega	M	1,000,000	$10^6$
Kilo	k	1,000	$10^3$
Hecto	h	100	$10^2$
Deca	da	10	$10^1$
-	-	1	$10^0$
Deci	d	0.1	$10^{-1}$
Centi	c	0.01	$10^{-2}$
Milli	m	0.001	$10^{-3}$
Micro	μ	0.0000001	$10^{-6}$
Nano	n	0.000000001	$10^{-9}$
Pico	p	0.00000000001	$10^{-12}$
Femto	f	0.0000000000001	$10^{-15}$
Atto	a	0.00000000000001	$10^{-18}$

Biology

I do not understand much on this field of study, but I'll try to dump it as much as possible...

Atoms, molecules and compounds

I have no idea.