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In mathematics, the domain or set of departure of a function is the set into which all of the input of the function is constrained to fall. It is the set X in the notation f: X → Y.

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a mathematical expression that relates two variables and is written in the form of an equation.

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an inverse operation is an operation that undoes what was done by the previous operation.

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an identity is an equality relating one mathematical expression A to another mathematical expression B,

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is a fact or a rule written with mathematical symbols.

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an extraneous solution (or spurious solution) is a solution, such as that to an equation, that emerges from the process of solving the problem but is not a valid solution to the problem.

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Two algebraic expressions are said to be equivalent if their values obtained by substituting the values of the variables are same.

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 a statement that asserts the equality of two expressions.

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a statement believed to be true based on observations.

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n mathematics, the absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign. Namely, |x| = x if x is positive, and |x| = −x if x is negative, and |0| = 0. For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3.