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Hence is a term used in mathematics to mean “in consequence” or “therefore.” It is used to draw a conclusion from a preceding statement or equation. For example, if someone were to say, “If x is equal to 5, hence x + 3 is equal to 8,” they are using the term hence to draw the conclusion that if x is equal to 5, then x + 3 must be equal to 8.

Hence is also used in mathematics to denote the “following” or “next” step in a sequence of equations or steps. For example, if someone were to say, “Let x = 5, hence x + 3 = 8,” they are using the term hence to denote that the following step is to add 3 to 5 to get 8.

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In addition to being used to draw conclusions and denote the next step in a sequence, hence can also be used to denote that a statement is true for any given value. For example, if someone were to say, “Let x be any real number, hence x + 3 is also a real number,” they are using the term hence to denote that the statement is true for any real number.

Hence can also be used to denote that a statement is true for all values of a given variable. For example, if someone were to say, “Let x be any real number, hence x^{2} + 3x + 1 is also a real number,” they are using the term hence to denote that the statement is true for all values of x.

Hence is an important term to understand in mathematics, as it is used to draw conclusions, denote the next step in a sequence, denote that a statement is true for any given value, and denote that a statement is true for all values of a given variable.