# Symbols

Important Common Maths Symbols

 Symbol Symbol Name Meaning Example + Plus sign Addition 2 + 3 = 5 − Minus sign Subtraction 3 − 2 = 1 × Times sign Multiplication 4 × 2 = 8 * Asterisk Multiplication 4 * 2 = 8 ∙ Multiplication dot Multiplication 4 ∙ 2= 8 ÷ Division sign Division 4 ÷ 2 = 2 / Division slash Division 4 / 2 = 2 – Horizontal line Division / fraction ± Plus - minus Both plus and minus operations 4 ± 3 = 7 and 1 ∓ Minus - plus Both minus and plus operations 4 ∓ 5 = -1 and 9 = Equals sign Equality 7 =  2 + 5 ≠ Not equal sign Inequality 3 ≠ 4 > Strict inequality Greater than 6 > 3 < Strict inequality Less than 4 < 7 ≥ Inequality Greater than or equal to 6 ≥ 4 ≤ Inequality Less than or equal to 3 ≤ 5 ( ) Parentheses Calculate expression inside first 4 × (3 + 2) = 20 [ ] Brackets Calculate expression inside first [(1 + 3) × (1 + 2)] = 12 . Period Decimal point, decimal separator 1.26 = 1 + 26/100 ab Power Exponent 33 = 27 Square root Cube root % Percent 1% = 1/100 10% × 50 = 5 ~ Approximately equal Weak approximation 10.7 ~ 10 ≈ Approximately equal Approximation x ≈ y means x is approximately equal to y ∝ Proportional to Proportional to y ∝  x when y = kx, where k is a constant ⇒ Implies This implies x = 2 ⇒  x2 = 4 ⇔ Equivalent If and only if (iff) ∀ For all ∀ x >1, x2 > x ∃ There exists ∃ x such that x2 > x ∴ Therefore a = b ∴ b=a ∵ Because / since Since a2 = 25, a = 5

Common Set Symbols

 Symbol Symbol Name Meaning Example { } Set A collection of elements A ={1, 2, 4, 5} B = {4, 5, 6} A ∪ B Union Objects that belong to set A or set B A ∪ B = {1, 2, 4, 5, 6} A ∩ B Intersection Objects that belong to set A and set B A ∩ B = {4, 5} A ⊆ B Subset Set A has fewer elements or equal to the set B {4, 5, 6} ⊆ B A ⊂ B Proper subset Set A has some elements of set B {4, 5} ⊂B A ⊄ B Not a subset Set A is not a subset of B {1, 6} ⊄ A A ⊇ B Superset Set A has more elements or equal to the set B {1, 2, 4, 5} ⊇{1, 2, 4, 5} A ⊃ B Proper superset Set A has more elements than set B {1, 2, 4, 5} ⊇{1, 2, 4} A ⊅ B Not a superset Set A is not a superset of set B {1, 2, 4, 5} ⊅{5, 7} A = B Equality Both sets A and B have the same members {1, 2, 4, 5} = (1, 2, 4, 5} A×B Cartesian product Set of all ordered pairs from A and B {1,2} × {3,4} = {(1,3), (1,4), (2,3), (2,4)} Ac Complement All the objects that do not belong to set A Ac = {3, 6} when U = {1, 2, 3, 4, 5, 6} A - B Difference Objects that belong to A and not to B {1, 2, 4, 5} − {4, 5} = {1,2} a∈A An element of The element a is in set A. 4 ∈ {1, 2, 4, 5} x∉A Not an element of The element a is not in set A. 6 ∉ {1, 2, 4, 5} |A| Cardinality The number of elements of set A A = {1, 2, 4, 5}, |A|=4 Ø Empty set Ø = { } {1, 2} ∩ {5 ,6} = Ø U Universal set Set of all possible values Normally, universal set in mathematics is the set of real numbers R. N Natural numbers N = {1, 2, 3, 4,...} 1 ∈ N W Whole numbers W = {0, 1, 2,3,4,5,...} 0 ∈ W Z Integer numbers set Z = {…-3, -2, -1, 0, 1, 2, 3…} -7 ∈ Z Q Rational numbers set Q = {x | x = a/b, a, b∈ Z } 2/5 ∈ Q R Real numbers set R = {x | -∞ < x <∞} 6.353535 ∈ R

Common Geometry Symbols

 Symbol Symbol Name Meaning Example ∠ Angle A figure formed by two rays. ∠ABC = 30o ∟ Right angle An angle which is equal to 90º. ∠ABC = 90o Δ Triangle Triangle shape ΔABC has  3 sides. o Degree 1 turn = 360 o 360° makes a full circle. Line Infinite line The infinite line that includes A and B: Line segment Line from point A to point B The line between A and B: Ray Line that start from point A The line that starts at A, goes through B and continues on: Arc Arc from point A to point B ⊥ Perpendicular Perpendicular lines (90º angle) AC ⊥ BC || Parallel Parallel lines AB || CD ≅ Congruent to Same shape and size ∆ABC ≅ ∆XYZ ~ Similarity Same shapes, not same size ∆ABC ~ ∆XYZ |x - y| Distance Distance between points x and y | x - y | = 5