User:Techit/Knowledge dump: Difference between revisions

Revision as of 20:18, 25 June 2025

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 = {1,2,3,4,5,6,7,8,9} or $Slave = {Diskette, GameCreator}$ .

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.

$A = {x | x \in 𝕀^{+}, - 5 < x \leq 12}$
$B = {x | x \in ℙ, - 5 \leq x \leq 23}$

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. $ℝ, ℚ, 𝕀, ℙ$ , these can be denotes to...

$ℝ$ = real numbers
$ℝ^{+}$ = positive real numbers
$ℝ^{-}$ = negative real numbers
$ℚ$ = rational numbers
$ℚ^{+}$ = positive real numbers
$ℚ^{-}$ = negative real numbers
$𝕀$ = integer numbers
$𝕀^{+}$ = positive integer numbers
$𝕀^{-}$ = negative integer numbers
$ℕ$ = natural numbers
$ℙ$ = 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 $n$ 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;

{} is called "empty set" or "null" in computer nerd language
$Ø$ can be used to represent empty set too
$A \in B ⟹ A \subseteq B$ is generally false too.

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. $P (A) = {Ø, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}$

@@ Line 2: / Line 2: @@
 == 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.
 === [[wikipedia:Set_(mathematics)|Set]] ===
@@ Line 7: / Line 8: @@
 ====== Elements / Members ======
-A stuff in a data set is called "element" or "member", so to write a set notation we use <math>\in</math>(in) or <math>\not\in</math>(not in). Let's see some examples below.
+A stuff in a data set is called "element" or "member", so to write a set notation we use <math>\in</math>(in). So let's see some examples below.
-<math>A=\{x|x\in I^{+}, -5<x\leq12 \}</math> or <math>B=\{x|x\in P, -5\leq x \leq 23\}</math>
+# <math>A=\{x|x\in \mathbb{I}^{+}, -5<x\leq12 \}</math>
+# <math>B=\{x|x\in \mathbb{P}, -5\leq x \leq 23\}</math>
+To translate set notation to normal human-being data set we look at <math>\in</math>then use our brain to analyze, after that A should be {x which x in <math>I^{+}</math> (positive integer), x greater than -5 but less or equals to 12}, which in conclusion to be <math>A=\{1,2,3,4,5,6,7,8,9,10,11,12\}</math>.
+Additional info: you might see these stupid blackboard letters e.g. <math>\mathbb{R}, \mathbb{Q}, \mathbb{I}, \mathbb{P}</math>, these can be denotes to...
+* <math>\mathbb{R}</math> = [[wikipedia:Real_number|real numbers]]
+* <math>\mathbb{R}^{+}</math> = positive real numbers
+* <math>\mathbb{R}^{-}</math> = negative real numbers
+* <math>\mathbb{Q}</math> = [[wikipedia:Rational_number|rational numbers]]
+* <math>\mathbb{Q}^{+}</math> = positive real numbers
+* <math>\mathbb{Q}^{-}</math> = negative real numbers
+* <math>\mathbb{I}</math> = [[wikipedia:Integer_number|integer]] numbers
+* <math>\mathbb{I}^{+}</math> = positive integer numbers
+* <math>\mathbb{I}^{-}</math> = negative integer numbers
+* <math>\mathbb{N}</math> = [[wikipedia:Natural_number|natural numbers]]
+* <math>\mathbb{P}</math> = [[wikipedia:Prime_number|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" (<math>\mathbb{U}</math>; 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 <math>A=\{1,2,3\}</math> the A's subset would be <math>\{\}, \{1\}, \{2\}, \{3\}, \{1,2\}, \{1,3\}, \{2,3\}, \{1,2,3\}</math>, if you don't see the pattern, this is the pattern <math>\{\}, \dotsm, A</math> where <math>\dotsm</math> is combination of every member from 1 member {1} to 2 {1,2} to 3 {1,2,3} members to <math>\text{n}</math> members. The total subset amount will be <math>n(A)*2</math>. In this example <math>n(A)</math> is 3 so we will have a total subset of 6.
+Here's what you might need to know more about subset;
+# {} is called "empty set" or "null" in computer nerd language
+# <math>\text{Ø}</math> can be used to represent empty set too
+# <math>A \in B \implies A \subseteq B</math> is generally false too.
+====== Power set ======
+Power set is related to subset; it's just a set of all subset in that set. Let's bring <math>A=\{1,2,3\}</math> guess what is <math>P(A)</math>? Yes. <math>P(A)=\{\text{Ø},\{1\},\{2\},\{3\},\{1,2\},\{1,3\},\{2,3\},\{1,2,3\}\}</math>