equivalently

Equivalently is an adverb used to indicate that a statement or quantity can be expressed in a form that is logically or mathematically equal to another. It marks a reformulation that preserves truth conditions and outcomes while presenting the same idea in a different way. In mathematics and logic, equivalence means that two statements, expressions, or representations hold the same truth value under the same assumptions. Equivalently is often used to introduce an alternative formulation, a proof step, or a transformation.

Common uses appear in mathematical proofs, logical arguments, and scientific writing. For example, the contrapositive shows a relationship of equivalence: a statement A implies B is equivalent to not B implying not A. When two statements are said to be equivalent, they are true under the same conditions and can be substituted for one another in reasoning. In more descriptive writing, equivalently can introduce a restatement that makes a concept clearer without changing its meaning.

Etymology and form: equivalently derives from the adjective equivalent, with the suffix -ly to form an adverb. The root is from Latin aequivalens, from aequus “equal” and valēns “valuing.” The term is common in formal and technical writing and is used to signal a precise, interchangeable formulation rather than a consequence or inference.

See also: equivalence, biconditional, contrapositive.