User:Techit/Knowledge dump - Revision history

Techit: add more example of statement

2025-07-09T11:39:08Z

add more example of statement

← Older revision		Revision as of 18:39, 9 July 2025
Line 65:		Line 65:

	==== Statement ====		==== Statement ====
	A statement is not your bank statements but an anything that can only be true or false (or boolean; for computer nerd)		A statement is not your bank statements but an anything that can only be true or false (or boolean; for computer nerd). These are the example of a statement:

			# 1 is a prime number. (false)
			# 2 is a prime number. (true)
			# Mushroom is a fungi (true)

	== Physics ==		== Physics ==

Techit: added mathematical logic to math field

2025-07-09T11:17:37Z

added mathematical logic to math field

← Older revision		Revision as of 18:17, 9 July 2025
Line 60:		Line 60:

	Imagine <math>\mathbb{U}=\{1,2,\dots,9\}</math> and <math>A=\{1,3,5,7\}</math> and <math>B=\{2,4,5,6\}</math> then <math>A' = \{2,4,6,8,9\}</math>.		Imagine <math>\mathbb{U}=\{1,2,\dots,9\}</math> and <math>A=\{1,3,5,7\}</math> and <math>B=\{2,4,5,6\}</math> then <math>A' = \{2,4,6,8,9\}</math>.

			=== [[wikipedia:Mathematical_logic\|Mathematical logic]] ===
			Mathematical logic is ตรรกศาสตร์ in Thai; ok? In this topic we will see more symbol to remember (more migraines).

			==== Statement ====
			A statement is not your bank statements but an anything that can only be true or false (or boolean; for computer nerd)

	== Physics ==		== Physics ==

Techit: /* Conversion */ fix spacing

2025-06-26T12:43:05Z

Conversion: fix spacing

← Older revision		Revision as of 19:43, 26 June 2025
Line 68:		Line 68:

	===== Conversion =====		===== Conversion =====
	This is very important, you need to know. Say you want to convert <math>3.56 * 10^{15}\ ng</math> (nano gram) to <math>kg</math> (kilo gram); what you need to do is you convert to the <math>ng</math> to <math>g</math> first. Take a look at the SI prefixes table below, multiply <math>3.5610^{15}</math> with the exponent of that converting prefix; "nano" here. <math>3.5610^{15}10^{-9}</math>, boom you got <math>3.5610^{6}\ g</math>. Next convert <math>g</math> to <math>kg</math> by dividing <math>3.5610^{6}\ g</math> by <math>10^{3}</math> (kilo), you got <math>\frac{3.5610^{6}}{10^{3}}</math>. Then you must invert the <math>10^{3}</math> to <math>10^{-3}</math> and from dividing to multiplying so you got <math>3.5610^{6} 10^{-3}</math>, and the final answer will be <math>3.56*10^{3}\ kg</math>.		This is very important, you need to know. Say you want to convert <math>3.56 * 10^{15}\ ng</math> (nano gram) to <math>kg</math> (kilo gram); what you need to do is you convert to the <math>ng</math> to <math>g</math> first. Take a look at the SI prefixes table below, multiply <math>3.5610^{15}</math> with the exponent of that converting prefix; "nano" here. <math>3.5610^{15}10^{-9}</math>, boom you got <math>3.5610^{6}\ g</math>.

			Next convert <math>g</math> to <math>kg</math> by dividing <math>3.5610^{6}\ g</math> by <math>10^{3}</math> (kilo), you got <math>\frac{3.5610^{6}}{10^{3}}</math>. Then you must invert the <math>10^{3}</math> to <math>10^{-3}</math> and from dividing to multiplying so you got <math>3.5610^{6} 10^{-3}</math>, and the final answer will be <math>3.56*10^{3}\ kg</math>.

	===== Metric prefix =====		===== Metric prefix =====

Techit: /* Scientific notation */

2025-06-26T12:42:14Z

Scientific notation

← Older revision		Revision as of 19:42, 26 June 2025
Line 66:		Line 66:
	==== Scientific notation ====		==== Scientific notation ====
	This is nothing much, just some number shorteners.		This is nothing much, just some number shorteners.

			===== Conversion =====
			This is very important, you need to know. Say you want to convert <math>3.56 * 10^{15}\ ng</math> (nano gram) to <math>kg</math> (kilo gram); what you need to do is you convert to the <math>ng</math> to <math>g</math> first. Take a look at the SI prefixes table below, multiply <math>3.5610^{15}</math> with the exponent of that converting prefix; "nano" here. <math>3.5610^{15}10^{-9}</math>, boom you got <math>3.5610^{6}\ g</math>. Next convert <math>g</math> to <math>kg</math> by dividing <math>3.5610^{6}\ g</math> by <math>10^{3}</math> (kilo), you got <math>\frac{3.5610^{6}}{10^{3}}</math>. Then you must invert the <math>10^{3}</math> to <math>10^{-3}</math> and from dividing to multiplying so you got <math>3.5610^{6} 10^{-3}</math>, and the final answer will be <math>3.56*10^{3}\ kg</math>.

	===== Metric prefix =====		===== Metric prefix =====

Techit: added biology

2025-06-26T12:24:42Z

added biology

← Older revision		Revision as of 19:24, 26 June 2025
Line 23:		Line 23:
	* <math>\mathbb{Q}^{+}</math> = positive rational numbers		* <math>\mathbb{Q}^{+}</math> = positive rational numbers
	* <math>\mathbb{Q}^{-}</math> = negative rational numbers		* <math>\mathbb{Q}^{-}</math> = negative rational numbers
	* <math>\mathbb{I}</math> = [[wikipedia:Integer_number\|integer]] ~~numbers~~		* <math>\mathbb{I}</math> = [[wikipedia:Integer_number\|integer numbers]]
	* <math>\mathbb{I}^{+}</math> = positive integer numbers		* <math>\mathbb{I}^{+}</math> = positive integer numbers
	* <math>\mathbb{I}^{-}</math> = negative integer numbers		* <math>\mathbb{I}^{-}</math> = negative integer numbers
Line 161:		Line 161:
	\|<math>10^{-18}</math>		\|<math>10^{-18}</math>
	\|}		\|}

			== 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.

Techit: added math more set operation, added physics metric prefixes

2025-06-26T10:51:28Z

added math more set operation, added physics metric prefixes

Show changes

Techit: change Q+ and Q- from real to rational (thanks to Diskette)

2025-06-25T13:49:37Z

change Q+ and Q- from real to rational (thanks to Diskette)

← Older revision		Revision as of 20:49, 25 June 2025
Line 21:		Line 21:
	* <math>\mathbb{R}^{-}</math> = negative real numbers		* <math>\mathbb{R}^{-}</math> = negative real numbers
	* <math>\mathbb{Q}</math> = [[wikipedia:Rational_number\|rational numbers]]		* <math>\mathbb{Q}</math> = [[wikipedia:Rational_number\|rational numbers]]
	* <math>\mathbb{Q}^{+}</math> = positive ~~real~~ numbers		* <math>\mathbb{Q}^{+}</math> = positive rational numbers
	* <math>\mathbb{Q}^{-}</math> = negative ~~real~~ numbers		* <math>\mathbb{Q}^{-}</math> = negative rational numbers
	* <math>\mathbb{I}</math> = [[wikipedia:Integer_number\|integer]] numbers		* <math>\mathbb{I}</math> = [[wikipedia:Integer_number\|integer]] numbers
	* <math>\mathbb{I}^{+}</math> = positive integer numbers		* <math>\mathbb{I}^{+}</math> = positive integer numbers

Techit: added basic set operations (not finished)

2025-06-25T13:46:41Z

added basic set operations (not finished)

← Older revision		Revision as of 20:46, 25 June 2025
Line 7:		Line 7:
	Imagine a [[wikipedia:Array_(data_structure)\|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 <math>\text{Slave}=\{\text{Diskette},\text{GameCreator}\}</math>.		Imagine a [[wikipedia:Array_(data_structure)\|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 <math>\text{Slave}=\{\text{Diskette},\text{GameCreator}\}</math>.

	====== Elements / Members ======		==== 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). So 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.

Line 29:		Line 29:
	* <math>\mathbb{P}</math> = [[wikipedia:Prime_number\|prime numbers]]		* <math>\mathbb{P}</math> = [[wikipedia:Prime_number\|prime numbers]]

	====== Venn diagram ======		==== 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.		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 ====
	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.		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.

Line 39:		Line 39:
	# {} is called "empty set" or "null" in computer nerd language		# {} is called "empty set" or "null" in computer nerd language
	# <math>\text{Ø}</math> can be used to represent empty set too		# <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.~~		# <math>A \subseteq B \iff \forall x\,(x \in A \Rightarrow x \in B)</math> - A is a subset of B if every element of A is also an element of B
			# <math>A \subset B \iff (A \subseteq B, A \ne B)</math> - A is a proper subset only if A is subset of B and A is not equals to B
			#

	====== Power set ======		==== 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>		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>

			==== Basic set operations ====

			===== [[wikipedia:Set_intersectionhttps://en.wikipedia.org/wiki/Set_intersection\|Intersection]] =====
			The intersection of two sets <math>A</math>⁠⁠ and <math>B</math> ⁠⁠ is a set denoted ⁠⁠<math>A \cap B</math> whose elements are those elements that belong to both <math>A</math>⁠⁠ and ⁠⁠<math>B</math>. That is,<math>{\displaystyle A\cap B=\{x\|x\in A\land x\in B\},}</math> where <math>\land</math> denotes [[wikipedia:Logical_and\|logical and]].

			--- hi, it's 8:46pm, thats it for today

Techit: Added set, subset and power set

2025-06-25T13:18:58Z

Added set, subset and power set

@@ Line 2: / Line 2: @@
 == Mathematics ==
 === [[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>

Techit: Removed TOC

2025-06-25T12:06:19Z

Removed TOC

← Older revision		Revision as of 19:06, 25 June 2025
Line 1:		Line 1:
	Hello, welcome to Techit's knowledge dump page. Here I will dump as many knowledge as possible for collection in the future use.		Hello, welcome to Techit's knowledge dump page. Here I will dump as many knowledge as possible for collection in the future use.

	~~Here's the table of contents~~

	== Mathematics ==		== Mathematics ==