Transcription
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 also be 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 + b - c or a - 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 a left superscript, it can denote the nth 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. Its 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 the 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 the greater or equal to sign.
Using two less than signs, we can denote the much less than sign. The same is true for the much greater than sign.
Empty set symbol denotes a set that contains no elements.
Number sign, also known as octoo or hashtag, usually denotes the cardinality of a set, which is essentially the number of elements in the set.
In symbol denotes membership in a set. Its 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 denotes set inclusion, but it is used for emphasizing that the sets can be equal. If we cross that line, we get a symbol that denotes 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 backslash. 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.
Or returns true if at least one of the operands is true.
And operator returns true only if both operands are true.
Exclusive or operator returns true if exactly one of the operands is true.
True denotes logical constant for True value or a statement that is always true.
False 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.
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 bold typeface 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 quaternions.
O denotes the set of octonions.
U denotes the universal set, which is a set that contains all possible values in a range.
Notation apostrophe is used to denote the derivative of a function. By adding the second apostrophe, 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 limit 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 represents 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 R 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.
Aleph is used to represent the cardinality of infinite sets. For example, Aleph null represents the cardinality of the set of natural numbers.
Cardinality of the continuum, 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 value.
Nearest integer function, as its name suggests, returns the nearest integer to a given value.
Single line represents the divisibility.
This line crossed represents non-divisibility.
Two lines denote parallelism, and those lines crossed represents non-parallelism.
Upside down T represents perpendicularity. Sometimes it can also mean that two numbers are co-prime.
Bar over two points represents a line segment between those points.
Arrow over two points represents a ray starting at the first point and ending at the second point.
Arrow pointing in both directions represents an infinite line passing through both points.