Useful Mathematical Symbols

Transcription

1 32 Useful Mathematical Symbols Symbol What it is How it is read How it is used Sample expression + * ddition sign OR Multiplication sign ND plus or times and x Multiplication sign times Sum of a few disjunction conjunction Multiplication sign times summation sign The summation of Sum of many or infinitely many = 8 ( + B) = * B 2 x 6 = 12 ( * B) = + B 4 x 2 = = 8 Integral sign The integral of x 2 dx = x 3 /3 + c double integral sign The double integral of f(x,y) dx dy Triple integral sign Line integral sign The triple integral of f(x,y,z) dx dy dz The line integral of F dx Surface integral sign The surface integral of F(x,y,z) dx dy - Subtraction sign Minus sign minus Negative ± Plus/minus sign plus or minus Dot product sign dot x Cross product sign cross Product sign The product of ^ Carat to the power of Difference of two, negative number Expression of range, error, or tolerance Scalar (dot) product of two vectors Vector (cross) product of two vectors Product of three up to infinitely many 2-6 = kbps ± 10% B = B x B = - (B x ) exponent 2 ^ 4 = 16

2 33! Exclamation factoriall Product of all positive integers up to a certain value 3! = 6 surd root of lgebraic expressions z = (x + y) square root The square root of lgebraic expressions 4 = ± 2 Continuation sign and so on up to and so on indefinitely Extension of sequence S = {1, 2, 3, } / Slash divided by over Division 3/4 = 0.75 Division sign divided by Division 3 4 = 0.75 % Percent percent Proportion = 3.2 Per mil per mil Proportion = 32 : Colon, ratio sign is to such that it is true that Division or ratio, following logical quantifier or used in defining a set 2:4 = 20:40 x : x > 4 and x < 5 x : x < 0 or x > -1 S = {x : x < 3} Vertical line such that it is true that Symbol following logical quantifier or used in defining a set x x > 4 and x < 5 x x < 0 or x > -1 S = {x x < 3} :: Double colon averaged with arithmetic mean 3 :: 11 = 7 lemniscate infinity increases without limit Infinite summations Infinite sequence Limit x : x < ( ) Parentheses quantity list set of coordinates open interval quantity, list, set of coordinates, or an open interval (x + y) + z (a 1, a 2, a 3, a 4) (x,y,z) (3,5) [ ] Square brackets the quantity the closed interval quantity or a closed interval w + [(x + y) + z] [2,4] ( ] Hybrid brackets the half-open interval [ ) Hybrid brackets the half-open interval half-open interval half-open interval (2,4] [2,4) { } Curly brackets the quantity the set quantity or a set E = {2, 4, 6, 8, }

3 34 = Equal sign equals are the same -(-6) = 6 2z 2 + 4z - 6 = 0 Proportionality sign is proportional to ~ Similarity sign is similar to pproximate equal sign is approximately equal to Inequality sign is not equal to < Inequality sign is less than Inequality sign is less than or equal to is at most equal to > Inequality sign is greater than Inequality sign absolute value sign increment sign, Triangle Perpendicularity is greater than or equal to The absolute value of the change in triangle is perpendicular to variables change in direct proportion objects are geometrically similar are close to each other x y BC ~ DEF x + y are different x y is smaller than is smaller than or equal to is larger than is larger than or equal to Distance of value from origin in number line, plane, or space Indicates a small change, Denotes vertices of triangle Geometry 2 < 4 x < y x y 4 > 1 x > y x y z -5 = 5 m = y / x BC = DEF L M // Parallel is parallel to Geometry L // M angle ngle Geometry BC = DEF Existential quantifier For some There exists a(n) x : x > 4 and x < 5 Universal quantifier For all For every x : x < 0 or x > -1

4 35 negation not ( ) logical implication implies If then B logical equivalence is logically equivalent to if and only if.. B Three dots therefore it follows that or mathematical proofs x = y and y = z x = z Element-of is an element of a set a Not-element-of is not an element of a set b Subset is a subset of B Proper subset is a proper subset of B Union union B = B Intersection intersect intersected with B = B Null Hebrew aleph (uppercase) The null set The empty set leph º Degree degree(s) = { } Transfinite cardinal ngular measure Temperature = 1 = 45º T = +20 ºC Greek theta Greek phi theta ngular variable = 90º phi ngular variable = 45º Greek lambda lambda wavelength Ratio Eigenvalue Lebesgue measure = 70 cm = 3:1 µ Greek mu Greek pi micro- (10-6 ) prefix multiplier C = µf pi General science Greek omega (uppercase) omega Volume of an object Ohms (resistance) R 2 = 330 Greek omega omega Transfinite ordinal ngular velocity Period = 36,000 rad/s = 1/60 s

5 36, N Enhanced or bold N The set of natural, Z Enhanced or bold Z The set of integers, Q Enhanced or bold Q The set of rational, R Enhanced or bold R The set of real = {0, 1, 2, 3, } = {0, 1, -1, 2, -2, 3, -3, } = {a/b a and b are in } What is the cardinality of?