Mathematics symbols - Algebraic

Mathematics Symbols are very important to learn mathematics, on using symbols we can easily understand. 

 Mathematics Symbols can be categorized on their importance in the following ways:

1. Mathematics symbols - Number
2. Mathematics symbols - Basic
3. Mathematics symbols - Algebraic
4. Mathematics symbols - Geometric
5. Mathematics symbols - Trigonometry
6. Mathematics symbols - Set Theory
7. Mathematics symbols - Statistics & Probability
8. Mathematics symbols - Calculus And Analysis
9. Mathematics symbols - Logical
10. Mathematics symbols - Roman
11. Mathematics symbols - Greek
12. Mathematics symbols - Miscellaneous

Now we shall learn /discuss Third topic Mathematics symbols - Algebraic on this post.

Mathematics symbols - Algebraic

 These are very important Basic Tools frequently used by us in algebra as well as in other branches of mathematics and sciences.

Symbol	Name of Symbol	Definition / Meaning	Illustration
Any alphabets like x or y or z	Variable x or variable y or etc...	The unknown value we have to find	If 4x = 4, then x = 1 or  If -12z = 48, then z = -4
≡	Equivalence (Used in Relation)	Identical to	a ≡ b, a is identical to b.
≜	Equal by definition	Equal by definition (that is given)	This symbol is also used for the same:=
:=	Equal by definition	Equal by definition (that is given)	This symbol is also used for the same ≜
~	Approximately equal	Weak approximation	11.0001 ~ 10.9999
≈	Approximately equal	Approximation (more near in comparison to ~ )	tan x≈ x if x is very small tan(0.001) ≈ 0.001 or  sin x≈ x if x is very small
∝	Proportional to	Proportional to ( If number varies in definite proportion)	y ∝ x when y = k x, where k is a proportionality constant.
∞	Lemniscate	Symbol of Infinity	it can be also used in both sense + ∞ and - ∞.
≪	Much less than	Much less than (Very)	1 ≪ 1000000
≫	Much greater than	Much greater than (Very)	1000000 ≫ 1
( )	parentheses	calculate expression inside first	-2 × (3+5) = -16
[ ]	brackets	calculate expression inside first	[(1+3)×(1+5)] = 24
{ }	Braces	Used for a set or known as Curley Bracket also	A = {a, e, i, o, u}
⌊x⌋	floor brackets	Rounds number to lower integer	⌊5.1⌋ = 5 =⌊5.9⌋  = ⌊5.7⌋ =⌊5.3⌋
⌈x⌉	Ceiling brackets	rounds number to upper integer	⌈4.3⌉ = 5
n!	Factorial / Exclamation mark	In mathematics used for Factorial Notation	1! =1 2! = 1*2= 2 3! = 1*2*3 = 6 4! = 1*2*3*4 = 24 ... n! = 1*2*3*4 ...   continued products upto n
| x |	Vertical bars	Absolute value in Real numbers and Modulas in Complex Numbers	| -4 | = 4 or | -3.2 | = 3.2 or | -101 | = 101.
f (x) or g(x)	function of x	Mappings values of x to f(x)	f (y) = 4y-3
(f ∘ g)	Composition of functions	(f ∘ g) (x) = f (g(x))	f (x)=3x,g(x)=x-1 ⇒(f ∘ g)(x)=3(x-1)
(a,b)	Interval Open	(a,b) = {y | a < y < b} Initial and final values are not incliuded	y ∈ (0,6)
[a,b]	Interval Closed	[a,b] = {y| a ≤ y ≤ b} Initial and final values are also incliuded	y ∈ [-4,4]
∆	Delta	Difference ( Used in Numerical Analysis and higher studies)	∆t = t1 - t0
∆	Discriminant	Δ = b2 - 4ac in quadratic equation where   a = coefficient of square of x b = coefficient of x  c = constant term	Used for finding Nature of Roots - Quadratic Equations
∑	Sigma used for Summation	Used for summation - the sum of all values in the range of series	∑ xi= x1+x2+...+xn
∑∑	sigma	double summation
∏	capital pi	Used for Product - Product of all values in range of series	∏ xi=x1∙x2∙...∙xn
e	Euler's number	e = 2.718281828...	e = lim (1+1/y)y , Where y→∞
	e constant	For logarithms	e = lim (1+1/y)y , Where y→∞