starting with the most basic symbols the plus sign is universally recognized as the symbol for addition minus sign which is essentially the opposite of the plus sign represents subtraction but it can also denote negative numbers multiplication sign is used to denote the operation of multiplying two numbers together and can also be represented as a DOT division sign signifies division the opposite of multiplication it can sometimes be written as a slash plus minus denotes either plus or minus sometimes it can be also used to denote a range of values its counterpart minus plus sign is used in conjunction with the plus minus sign it denotes the opposite sign of plus minus for example this expression means that it's either a plus B minus C or a minus B+ C both signs can't be the same the root symbol denotes the square root of a number with an integer greater than two as left superscript it can denote the N root of a number the equal sign represented by two lines which are equal in length is used to denote the equality between two expressions the opposite of the equal sign is the not equal sign which indicates that two expressions are not equal approximately equal sign is used when two values are not exactly equal but are close enough instead of approximately equal sign we can also use Tilda but Tilda also denotes similarity or proportionality this symbol that looks like an unfinished Infinity also represents proportionality the triple bar or the equivalent sign can be used to denote an identity but its more common use is to denote congruence in modular arithmetic the less than symbol is used to indicate that one quantity is smaller than another it's opposite the greater than sign is used to indicate that one quantity is larger than another if we add a line to the less than symbol we get less than or equal sign as the name suggests it indicates that one value is smaller or equal to another the same is true for greater or equal to sign using two less than signs we can denote much less than sign the same is true for much greater than sign empty set symbol denotes a set that contains no elements number sign also known as octoo or hashtag usually denotes cardinality of a set which is essentially the number of elements in the set in symbol denotes membership in a set it's opposite not in symbol denotes that an element is not a member of the set the set inclusion sign represents that one set is a subset of another set if we add a line we get a symbol that also notes set inclusion but it is used for emphasizing that the sets can be equal if we cross that line we get a symbol that Den notes a proper subset meaning that the sets are not equal union represents an operation of combining two sets which results in another set containing all unique elements from both sets intersection denotes another operation of combining two sets the result of intersection is a set which contains elements that are common in both sets set difference is denoted by a backslab the result of this operation is a set which contains all elements of the first set that are not in the second set symmetric difference can be denoted by a triangle or a circled minus the result of this operation is the set that contains all elements that belong to exactly one of the two sets negation symbol is used in logic to indicate the opposite of a statement or operator returns true if at least one of the operant is true and operator returns true only if both oper are true exclusive or operator returns true if exactly one of the operand is true T denotes logical constant for True Value or a statement that is always true uptech represents logical constant for false value or a statement that is always false Universal quantifier asserts that a statement is true for all elements in a given domain the existential quantifier asserts that there exists at least one element in a given domain for which a particular statement holds true uniqueness quantifier is used to assert that there's exactly one element in a given domain for which a particular statement holds true conditional operator denotes an implication between two statements if the first statement is true then the second is also true a logical equivalence operator indicates that two statements have the same logical value the capital letters written in Blackboard bolt type face usually denote the basic number systems n denotes the set of natural numbers Z denotes the set of integers Q denotes the set of rational numbers R denotes the set of real numbers C denotes the set of complex numbers H denotes the set of quaternion O denotes the set of octonian U denotes the universal set which is a set that contains all possible values in L range's notation apost is used to denote the derivative of a function by adding the second ostr we can denote the second derivative the third for the third derivative and so on in Newton's notation the derivative is denoted as a dot it is usually used to denote a derivative of a variable with respect to time adding the second dot we can represent the second derivative the liit notation for derivative represents the derivative of a function or a variable at the top with respect to the variable at the bottom if we round the D we get a notation that represents the partial derivative it is used for a function of several variables integral denotes an anti- derivative which is basically the opposite of the derivative with subscript and superscript it denotes a definite integral which represent the area under a curve or the accumulation of a quantity over an interval arrow is sometimes used to define a function without having to name it function composition is an operation that combines two functions logarithm is an inverse operation of exponentiation subscript denotes the base of the logarithm log without a subscript represents the logarithm with base 10 the natural logarithm denoted as Ln represents a logarithm with base e limit is used to denote the behavior of a function or an expression as its input approaches a certain value the fancy art denotes the real part of a complex number the fancy I denotes the imaginary part of a complex number using a bar above a complex number we can denote the complex conjugate of that number which just changes the sign of the imaginary part of the number Greek letter Sigma is used to denote summation of a series of terms Capital Pi works the same as Sigma but it denotes a product infinity symbol denotes a concept of unlimitedness it signifies a value that is greater than any finite quantity Alf is used to represent the cardinality of infinite sets for example Alf null represents the cardinality of the set of natural numbers fractor C also denotes a type of infinity it represents the cardinality of the set of real numbers factorial is an operation that multiplies a number by all positive integers smaller than that number binomial coefficient looks like a fraction without the line but it represents the number of ways to choose K elements from a set of n elements absolute value of a number represents the distance of that number from zero on the number line the floor function Returns the greatest integer less than or equal to the value on the other hand the ceiling function Returns the smallest integer larger than or equal to the the value nearest integer function as its name suggests Returns the nearest integer to a given value single line represents the visibility this line crossed represents non- divisibility two lines denote parallelism and those lines crossed represents nonp parallelism upside down T represents perpendicularity sometimes it can also mean that two numbers are co- Prime Bar over two points represent a line segment between those points Arrow over two points represents array starting at the first point and ending at the second Point arrow pointing in both directions represents an infinite line passing through both points