ligeværdige

Ligeværdige is a Danish adjective meaning having equal value or worth. The term is used in mathematical, logical, and everyday contexts to describe quantities, expressions, or statements that share the same value or significance. It is formed from lig(e) meaning equal and værdige or værdi relating to value.

In mathematics, ligeværdige describes two expressions or formulas that evaluate to the same quantity for all permissible values of the variables. For example, the expressions 2x + 2 and 2(x + 1) are ligeværdige because they simplify to the same expression, 2x + 2, for any x in the domain. The concept underpins algebraic manipulation, simplification, and verification of identities.

In logic, ligeværdige can refer to statements that are logically equivalent, meaning each statement implies the other. For instance, p → q and ¬p ∨ q are considered ligeværdige in classical logic, because they have the same truth value in every possible scenario.

In everyday language, ligeværdige is used to denote that two objects, prices, or situations have equal value or merit. The term emphasizes parity in worth rather than relative superiority.

Related concepts include equality, equivalence, and logical equivalence, all of which address the idea of sameness in value or truth under different contexts. Ligeværdige thus serves as a versatile term across mathematics, logic, and everyday discourse to denote equal value.