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Mathematical Notation

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\forall

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Universal quantification; denotes 'for all' or 'for any' within a given context.

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\supset

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Superset; denotes a set that contains all elements of another set.

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\exists

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Existential quantification; denotes the existence of at least one element that satisfies a given property.

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\lor

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Logical disjunction; denotes 'or', used to combine two statements where at least one must be true.

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\therefore

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Therefore; used before a logical conclusion that follows from the arguments provided.

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\int

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Integral; represents the area under a curve or the antiderivative of a function.

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\equiv

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Equivalence; denotes that two expressions are identically equal or congruent.

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\cong

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Congruent; used to denote that two figures have the same shape and size.

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\in

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Element of; denotes membership of an element in a set.

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\ni

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Contains as an element; denotes that a set has a particular element.

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\nabla

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Del or nabla operator; used in vector calculus to denote gradient, divergence, or curl.

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\Rightarrow

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Material implication; denotes 'implies that' in logical statements.

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\Leftrightarrow

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Material equivalence; denotes 'if and only if' and establishes that two statements are both necessary and sufficient for each other.

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\prod

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Product notation; indicates the multiplication of a sequence of terms.

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\sum

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Summation; denotes the sum of a sequence of terms.

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ddx\frac{d}{dx}

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Derivative; denotes the rate at which a function is changing at any given point.

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x\frac{\partial}{\partial x}

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Partial derivative; indicates the derivative of a function with respect to one of many variables, treating the others as constants.

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\parallel

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Parallel; indicates that two lines, segments, or planes are equidistant and will never meet.

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¬\neg

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Negation; denotes the logical complement of a statement.

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\land

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Logical conjunction; denotes 'and', used to combine two statements that must both be true.

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\sim

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Similar; used to denote geometrical similarity, meaning the figures have the same shape but not necessarily the same size.

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ABC\angle ABC

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Denotes the angle formed by points A, B, and C, with the vertex at point B.

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lim\lim

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Limit; calculates the value that a function approaches as the variable approaches a specified value.

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\emptyset

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Empty set; denotes a set with no elements.

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\oplus

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Direct sum; refers to the sum of algebraic structures, such as groups, rings, and vector spaces.

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\subseteq

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Subset or equal to; denotes all the elements of one set are contained within another, and the sets may be equal.

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\perp

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Perpendicular; denotes that lines, segments, or planes meet at a right angle (90 degrees).

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\subset

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Subset; denotes that all elements of one set are contained within another set.

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Δ\Delta

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Delta; represents change or difference in mathematical expressions.

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\otimes

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Tensor product; operation on two tensors that produces another tensor.

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