Math - Revision history

Civvy: Rewrite introduction to clarify what mathematics is and provide a link for the user to view basic mathematics.

2025-12-19T00:21:49Z

Rewrite introduction to clarify what mathematics is and provide a link for the user to view basic mathematics.

← Older revision		Revision as of 00:21, 19 December 2025
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	~~Math, Maths or~~ Mathematics, is the ~~term used for~~ the ~~science of numbers~~, ~~whether just for the purpose of discoveries~~ and ~~knowledge of Math (Pure Mathematics) or to be used in other fields (Applied Mathematics)~~.		'''Mathematics''' is a system of measuring the properties in the world around us. At its core, it is about noticing patterns, comparing things, and describing relationships between objects and concepts.

	== ~~Counting and~~ Numbers ==		If you need help with basic mathematics, please see [[Basic Mathematics]] for more information.

			== Numbers ==
	Numbers are explained best to beginners as how many of an object there are: a farmer may be sad he only has '''one''' cow, if someone gave him another cow he would have '''two''' cows.		Numbers are explained best to beginners as how many of an object there are: a farmer may be sad he only has '''one''' cow, if someone gave him another cow he would have '''two''' cows.

Catzcute4: more math!

2025-08-05T13:30:14Z

more math!

← Older revision		Revision as of 13:30, 5 August 2025
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	The use of numbers allows people to describe and predict the real world, for science, computers, trade, records and almost any field that needs description.		The use of numbers allows people to describe and predict the real world, for science, computers, trade, records and almost any field that needs description.

	Whole numbers or '''~~integers~~''' can be described by increasing them by one, known as counting.		Whole numbers or '''naturals''' (ℕ) can be described by increasing them by one, starting at 0, known as counting. Mathematically, counting is a successor (S(a), where a is a number), and S(a) is a number is a is a number, if S(a) = S(b) then a = b (and other way around), and no natrual number, a, exists such that S(a) = 0.

			In base 10, we count with the ones digit (0, 1, 3, 4, 5, 6, 7, 8, 9), but once we have to count from 9, we go to 0 and increase the digit to its left by 1 (if there is no digit, set it to 1). If ''that'' digit is at 9, we use another digit (ex. 99, 100). An example is shown below.

	=== Counting Numbers Up To Fourteen ===		=== Counting Numbers Up To Fourteen ===
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	Thirteen 13		Thirteen 13

	Fourteen 14...		Fourteen 14

			There are more numbers, in fact infinitely. If negative numbers are allowed (such n + -n = 0, where n is a natural number), we can “negate” a number and get integers (ℤ). We can use rational numbers (ℚ) by allowing the division of any number by any other number, as long as the 2nd number isn’t 0. Real numbers (ℝ) exist to fill in the “gaps” (ex. sqrt(2)), and complex numbers (ℂ) are defined where i*i = -1. There are more number systems out there, but those are the most common ones.

	== Mathematical Symbols ==		== Mathematical Symbols ==
	There are some symbols that are utilized in Mathematics ~~that are not found elsewhere~~, such as:		There are some symbols that are utilized in Mathematics, such as:

	* = : The equals sign. This symbol means that the values of the numbers on both sides of it are the same.		* A=B : The equals sign. This symbol means that the values of the numbers on both sides of it are the same. It is symmetric (A=B implies B=A), reflexive (A=A), and transitive (A=B and A=C implies A=C).
	* + : The plus sign. This means that the values of the numbers on either sides are going to be combined.		* A≈B : Approximately equals. It is symmetric and reflexive, but not transitive. If A is not used, it is an approximate value.
	* - : The minus sign. This means that the value of one number is going to be removed from the other.		* A+B : The plus sign. This means that the values of the numbers on either sides are going to be combined. In the natural numbers, A + 0 = B and A + S(B) = S(A+B).
	* % : The percent sign. This dictates that the number preceding it is a percentage of something out of 100.		* A-B : The minus sign. This means that the value of one number is going to be removed from the other, or, if A is not used, B is negated (ex. -(5) = -5 and -(-5) = 5).
	* * or x or ⋅ : The multiplication or "times" sign. This means that the values of the numbers on either sides of it are going to be multiplied together, ~~making a larger value~~.		* A%B : The percent sign. This dictates that the number preceding it is a percentage of something out of 100 or a remainder.
	* / or ÷ : The division sign. This means that the value of the numbers are going to be reduced by how many times one number can be put into the other.		* * or × or ⋅ or AB: The multiplication or "times" sign. This means that the values of the numbers on either sides of it are going to be multiplied together, repeated addition. A and B represent numbers. In the natural numbers, A×0 = 0 and A×S(B) = A×B + A.
			* A/B or ÷ : The division sign. This means that the value of the numbers are going to be reduced by how many times one number can be put into the other. Note that any two numbers can be divided (unless the 2nd number is 0), but you will not always get an integer.
			* ^ or A<sup>B</sup> : The exponent sign. This is repeated multiplication. In the natural numbers, A<sup>0</sup> = 1 and A<sup>S(B)</sup> = A<sup>B</sup> × A.
			* √a or <sup>B</sup>√A : A square root (if b isn’t used), or a bth root if b is used, of a. This is one way to reverse exponents.
			* log<sub>b</sub>(A) or log(A) or ln(A) : A logarithm, which is another way to reverse exponents. log<sub>b</sub>(a) is log base b, log(a) is log<sub>10</sub>(a), and ln(a) is log<sub>e</sub>(a), where e ≈ 2.7182818285…
			* ↑ : A knuth up arrow. One up arrow (A↑B) is exponentiation, and adding more up arrows repeats more: A↑↑B is repeated exponents (tetration), a↑↑↑b is repeated tetration (pentation), and so on. It should be of note that a↑<sup>C</sup>B is a[c up arrows]b, where C is any natural number.
			* A∧B or A&B : And. Only true if both A and B are true.
			* A∨B or A\|B : Or. Only true if at least one of A or B is true.
			* ¬A or ~A : Not. Only true if A is false. If ~ is used, may also mean an approximate value.
			* A⇒B or A→B : Implies. Only false if A is true and B is false.
			* A⇔B or A⟷B : Iff or if and only if. Only true if A is true and B is true or A is false and B is false, like an equals sign.
			* ∀A:B : Universal quantifier. For all A, B is true.
			* ∃A:B : Existential quantifier. There exists an A such that B is true.
			* ∃!A:B : Uniqueness quantifier. There exists exactly 1 A such that B is true.
			* A∈B : In. A is in B.
			* A∪B : Union. The set containing all elements from A and all elements from B.
			* A∩B : Intersection. The set containing all elements in A that are also in B.

	== Basic Mathematical Functions ==		== Basic Mathematical Functions ==

	=== Succession ===		=== Succession ===
	Increases the value of a number by one, also known as counting. After one ~~comes two~~.		Increases the value of a number by one, also known as counting. After zero comes one.

	=== Addition ===		=== Addition ===
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	Decreases the value by how many times that value can go into it. Ten divided by two is five, or ''10 ÷ 2 = 5.''		Decreases the value by how many times that value can go into it. Ten divided by two is five, or ''10 ÷ 2 = 5.''

	Division is equivalent to inverse multiplication: ''5 * 3 = 15'', and then ''15 ÷ 3 = 5.''		Division is equivalent to inverse multiplication: ''5 * 3 = 15'', and then ''15 ÷ 3 = 5.''

	===~~= A Division Example in Story Form =~~===		=== Mod ===
	~~It is also easily visualized by imagining one is at~~ a ~~meal (bread and cheese), and that each person must receive an equal portion. To achieve this requires~~ division, ~~so you go~~ around ~~the table handing out pieces of bread and cheese one at a time, but suddenly..~~. ~~you have one portion of bread and cheese remaining to distribute to five people, there are two basic options:~~		The remainder of a division, loops numbers around.

	~~# Leave a ''"''Remainder''"'' for the host, letting them keep the extra bread and cheese all to themselves.~~		=== Exponents ===
	~~# Split the last portion of bread and cheese in five to share evenly, making <sup>1</sup>/<sub>5</sub> portions (one fifth or 0.2 of a portion)~~.		Repeated multiplication.

	== Advanced Mathematics ==		== Advanced Mathematics ==
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	=== Constants ===		=== Constants ===
	Closely related to axioms are the less fundamental constants, simply put these are values that are extremely common to the point that they are assigned a Mathematical/Alphabetical symbol.		Closely related to axioms are the less fundamental constants, simply put these are values that are extremely common to the point that they are assigned a Mathematical/Alphabetical symbol.

			=== Variables ===
			Also assigned letters or symbols. Can represent an constant unknown or a number that is not constant.

	=== List of Mathematical Constants ===		=== List of Mathematical Constants ===
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	\|ratio of a circle's circumference divided by its diameter		\|ratio of a circle's circumference divided by its diameter
	\|Determining the area of circles using diameter		\|Determining the area of circles using diameter
	\|~3.~~141592654~~		\|~3.1415926535…
	\|-		\|-
	\|~~'''c'''~~		\|τ
	\|C		\|Tau
	\|~~speed~~ of ~~light~~		\|ratio of a circles circumference divided by its radius, or 2π
	\|Finding the time it takes radio waves to reach mars		\|Finding the time it takes radio waves to reach mars
	\|~~299,792,458 m/s~~		\|~6.2831853072
	\|-		\|-
	\|'''ί'''		\|'''ί'''
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	\|the imaginary number or √-1		\|the imaginary number or √-1
	\|The solution to x² + 4x + 5 = 0 is x = -2 ± i.		\|The solution to x² + 4x + 5 = 0 is x = -2 ± i.
	\|~~N/A~~		\|i
	\|-		\|-
	\|'''e'''		\|'''e'''

PangeaReunion: Added "See Also" section

2025-05-22T22:10:09Z

Added "See Also" section

← Older revision		Revision as of 22:10, 22 May 2025
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	* An [[abacus]] is an analog calculator for basic arithmetic.		* An [[abacus]] is an analog calculator for basic arithmetic.

			== See Also ==

			* [[Geometry]]
			* [[Trigonometry]]

	[[Category:Maths]]		[[Category:Maths]]

Darthjaffacake: Added a section on algorithms which I will link to a new page on the subject

2025-05-18T22:57:47Z

Added a section on algorithms which I will link to a new page on the subject

← Older revision		Revision as of 22:57, 18 May 2025
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	=== Axioms ===		=== Axioms ===
	Axioms are the most fundamental aspect of Mathematics, being the basic rules that are assumed to be always true. Most separate categories of Math are made distinct by additional or altered axioms being present, the most noticed example being in lower level Physics<ref>[[:Category:Physics]]</ref> where additional axioms are added to account for universal Laws and context based simplification.		Axioms are the most fundamental aspect of Mathematics, being the basic rules that are assumed to be always true. Most separate categories of Math are made distinct by additional or altered axioms being present, the most noticed example being in lower level Physics<ref>[[:Category:Physics]]</ref> where additional axioms are added to account for universal Laws and context based simplification.

			=== Algorithms ===
			Algorithms are sets of instructions or rules that allow mathematical problems to be solved, like the result of a hard to calculate function or the value of a '''constant'''.

	=== Constants ===		=== Constants ===

PangeaReunion: Added values to list of constants

2025-05-18T16:10:34Z

Added values to list of constants

← Older revision		Revision as of 16:10, 18 May 2025
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	!Origin		!Origin
	!Example usage		!Example usage
			!Value (Rounded to 10 digits)
	\|-		\|-
	\|'''π'''		\|'''π'''
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	\|ratio of a circle's circumference divided by its diameter		\|ratio of a circle's circumference divided by its diameter
	\|Determining the area of circles using diameter		\|Determining the area of circles using diameter
			\|~3.141592654
	\|-		\|-
	\|'''c'''		\|'''c'''
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	\|speed of light		\|speed of light
	\|Finding the time it takes radio waves to reach mars		\|Finding the time it takes radio waves to reach mars
			\|299,792,458 m/s
	\|-		\|-
	\|'''ί'''		\|'''ί'''
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	\|the imaginary number or √-1		\|the imaginary number or √-1
	\|The solution to x² + 4x + 5 = 0 is x = -2 ± i.		\|The solution to x² + 4x + 5 = 0 is x = -2 ± i.
			\|N/A
	\|-		\|-
	\|'''e'''		\|'''e'''
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	\|The value that (1 + 1/n)<sup>n</sup> trends towards		\|The value that (1 + 1/n)<sup>n</sup> trends towards
	\|Exponential growth or decay using ex		\|Exponential growth or decay using ex
			\|~2.718281828
	\|-		\|-
	\|'''''φ'''''		\|'''''φ'''''
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	\|The ratio between two numbers next to each other in the Fibonacci sequence		\|The ratio between two numbers next to each other in the Fibonacci sequence
	\|Finding a Fibonacci number without calculating every previous number		\|Finding a Fibonacci number without calculating every previous number
			\|~1.618033989
			\|}

			=== Useful Approximations ===
			Some mathematical functions are difficult or impossible to calculate by hand, so it is useful to instead use an easier function that will give a value close to the real answer.
			{\| class="wikitable"
			\|+
			!Function
			!Approximation
			!Notes
			\|-
			\|'''sin(θ)'''
			\|θ - θ<sup>3</sup>/3! + θ<sup>5</sup>/5! - θ<sup>7</sup>/7! + …
			\|The more terms that you add, the more accurate the approximation will be for larger numbers.
			\|-
			\|'''cos(θ)'''
			\|1 - θ<sup>2</sup>/2! + θ<sup>4</sup>/4! - θ<sup>6</sup>/6! + …
			\|Same note as above
	\|}		\|}
	<references />		<references />

131.231.122.15: Added sections to do with numbers and counting and made changes to the way functions are described.

2025-05-18T14:35:43Z

Added sections to do with numbers and counting and made changes to the way functions are described.

@@ Line 1: / Line 1: @@
-Math, or Mathematics, is the term used for the science of numbers, whether just for Math (Pure Mathematics) or to be used in other fields (Applied Mathematics).
+Math, Maths or Mathematics, is the term used for the science of numbers, whether just for the purpose of discoveries and knowledge of Math (Pure Mathematics) or to be used in other fields (Applied Mathematics).
 == Mathematical Symbols ==
@@ Line 8: / Line 46: @@
 * - : The minus sign. This means that the value of one number is going to be removed from the other.
 * % : The percent sign. This dictates that the number preceding it is a percentage of something out of 100.
-* *  or x : The multiplication or "times" sign. This means that the values of the numbers on either sides of it are going to be multiplied together, making a larger value.
+* *  or x or ⋅ : The multiplication or "times" sign. This means that the values of the numbers on either sides of it are going to be multiplied together, making a larger value.
 * / or ÷ : The division sign. This means that the value of the numbers are going to be reduced by how many times one number can be put into the other.
-== Basic Mathematics ==
+== Basic Mathematical Functions ==
 === Succession ===
-Succession is a function that increases the value of a number by one. After one comes two.
+Increases the value of a number by one, also known as counting. After one comes two.
 === Addition ===
-Addition is the act of adding one number to another. One and one is two, or ''1+1=2''.
+Increases the value of one number by another number. Two and three is five, or ''2 + 3 = 5''.
 === Subtraction ===
-Subtraction is the act of removing value from a number. Five taken away from six is one, or ''6-5=1''.
+Decreases value from a number. Five subtracted from six is one, or ''6 '''–''' 5 = 1''.
 === Multiplication ===
-Multiplication is the act of multiplying one number's value by another, or increasing the value by that many times. Five multiplied by two is ten, or ''5*2=10''. This is often said as "times", or "five times two", as in "if you take five two times, you have ten".
+Increases value by that many times. Five multiplied by three is fifteen, or ''5 * 3 = 15''. This is often said as "times", or "five times three", as in "if you take five three times, you have fifteen".
-It is also easily interpreted as repeated addition, using the previous example; ''5*2''. We can add five, two times: ''5+5 = 10'', '''OR''' we can add two, five <u>times</u>, ''2+2+2+2+2= 10''.
+Multiplication is equivalent to repeated addition, ''5 * 3 = 5 + 5 + 5 = 15.''
 === Division ===
-Division is the act of dividing a number's value by another, or reducing the value to how many times that value can go into it. Ten divided by two is five, or 10/2=5.
+Decreases the value by how many times that value can go into it. Ten divided by two is five, or ''10 ÷ 2 = 5.''
 ==== A Division Example in Story Form ====
@@ Line 45: / Line 89: @@
 === Constants ===
-Closely related to axioms are the less fundamental constants, simply put these are values that are extremely common to the point that they are assigned a Mathematical/Alphabetical symbol. Common examples include; the ratio of a circle's circumference divided by its diameter: ''π'', the speed of light: ''c'', the imaginary number: ''ί,'' Euler's number: ''e'', and the golden ratio: ''φ''.
+Closely related to axioms are the less fundamental constants, simply put these are values that are extremely common to the point that they are assigned a Mathematical/Alphabetical symbol.
 <references />

Darthjaffacake: added division sign ÷ and described succession before addition

2025-05-18T11:09:41Z

added division sign ÷ and described succession before addition

← Older revision		Revision as of 11:09, 18 May 2025
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	* % : The percent sign. This dictates that the number preceding it is a percentage of something out of 100.		* % : The percent sign. This dictates that the number preceding it is a percentage of something out of 100.
	* * or x : The multiplication or "times" sign. This means that the values of the numbers on either sides of it are going to be multiplied together, making a larger value.		* * or x : The multiplication or "times" sign. This means that the values of the numbers on either sides of it are going to be multiplied together, making a larger value.
	* / : The division sign. This means that the value of the numbers are going to be reduced by how many times one number can be put into the other.		* / or ÷ : The division sign. This means that the value of the numbers are going to be reduced by how many times one number can be put into the other.

	== Basic Mathematics ==		== Basic Mathematics ==

			=== Succession ===
			Succession is a function that increases the value of a number by one. After one comes two.

	=== Addition ===		=== Addition ===

CarsonBoardman at 15:57, 10 May 2025

2025-05-10T15:57:26Z

← Older revision		Revision as of 15:57, 10 May 2025
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	Closely related to axioms are the less fundamental constants, simply put these are values that are extremely common to the point that they are assigned a Mathematical/Alphabetical symbol. Common examples include; the ratio of a circle's circumference divided by its diameter: ''π'', the speed of light: ''c'', the imaginary number: ''ί,'' Euler's number: ''e'', and the golden ratio: ''φ''.		Closely related to axioms are the less fundamental constants, simply put these are values that are extremely common to the point that they are assigned a Mathematical/Alphabetical symbol. Common examples include; the ratio of a circle's circumference divided by its diameter: ''π'', the speed of light: ''c'', the imaginary number: ''ί,'' Euler's number: ''e'', and the golden ratio: ''φ''.
	<references />		<references />

			== Mathematical tools ==

			* An [[abacus]] is an analog calculator for basic arithmetic.

	[[Category:Maths]]		[[Category:Maths]]

Mathematician: Added category. We'll need it.

2025-05-06T05:04:18Z

Added category. We'll need it.

← Older revision		Revision as of 05:04, 6 May 2025
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	=== Constants ===		=== Constants ===
	Closely related to axioms are the less fundamental constants, simply put these are values that are extremely common to the point that they are assigned a Mathematical/Alphabetical symbol. Common examples include; the ratio of a circle's circumference divided by its diameter: ''π'', the speed of light: ''c'', the imaginary number: ''ί,'' Euler's number: ''e'', and the golden ratio: ''φ''.		Closely related to axioms are the less fundamental constants, simply put these are values that are extremely common to the point that they are assigned a Mathematical/Alphabetical symbol. Common examples include; the ratio of a circle's circumference divided by its diameter: ''π'', the speed of light: ''c'', the imaginary number: ''ί,'' Euler's number: ''e'', and the golden ratio: ''φ''.
			<references />
			[[Category:Maths]]

Mathematician: Renamed Section: Complex Math --> Advanced Mathematics, Added to Section: Advanced Mathematics

2025-05-06T03:47:26Z

Renamed Section: Complex Math --> Advanced Mathematics, Added to Section: Advanced Mathematics

← Older revision		Revision as of 03:47, 6 May 2025
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	Math, or ~~mathematics~~, is the term used for the science of numbers.		Math, or Mathematics, is the term used for the science of numbers, whether just for Math (Pure Mathematics) or to be used in other fields (Applied Mathematics).

	== Mathematical ~~symbols~~ ==		== Mathematical Symbols ==
	There are some symbols that are utilized in ~~mathematics~~ that are not found elsewhere, such as:		There are some symbols that are utilized in Mathematics that are not found elsewhere, such as:

	* = : The equals sign. This symbol means that the values of the numbers on both sides of it are the same.		* = : The equals sign. This symbol means that the values of the numbers on both sides of it are the same.
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	* / : The division sign. This means that the value of the numbers are going to be reduced by how many times one number can be put into the other.		* / : The division sign. This means that the value of the numbers are going to be reduced by how many times one number can be put into the other.

	== Basic ~~math~~ ==		== Basic Mathematics ==

	=== Addition ===		=== Addition ===
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	# Split the last portion of bread and cheese in five to share evenly, making <sup>1</sup>/<sub>5</sub> portions (one fifth or 0.2 of a portion).		# Split the last portion of bread and cheese in five to share evenly, making <sup>1</sup>/<sub>5</sub> portions (one fifth or 0.2 of a portion).

	== ~~Complex math~~ ==		== Advanced Mathematics ==
	Functions. ~~Graphs~~. ~~Parabola~~.
			=== Functions ===
			Functions are a part of Mathematics that describe the action(s) preformed on an "input". The result of a function is an "output". Any Mathematical operation done is a form of function, including counting (referred to formally as succession). There are many ways to represent functions, the most common being; '''Function Notation, Algebraic, Graphical,''' within a '''Table,''' or using '''Natural Language'''.

			=== Axioms ===
			Axioms are the most fundamental aspect of Mathematics, being the basic rules that are assumed to be always true. Most separate categories of Math are made distinct by additional or altered axioms being present, the most noticed example being in lower level Physics<ref>[[:Category:Physics]]</ref> where additional axioms are added to account for universal Laws and context based simplification.

			=== Constants ===
			Closely related to axioms are the less fundamental constants, simply put these are values that are extremely common to the point that they are assigned a Mathematical/Alphabetical symbol. Common examples include; the ratio of a circle's circumference divided by its diameter: ''π'', the speed of light: ''c'', the imaginary number: ''ί,'' Euler's number: ''e'', and the golden ratio: ''φ''.