If a function that is not [[injective]] is applied to both sides of a true equation, then the resulting equation will still be true, but it may be less useful. Formally, one has an [[Logical conditional|implication]], not an [[Logical biconditional|equivalence]], so the solution set may get larger. The functions implied in properties (1), (2), and (4) are always injective, as is (3) if we do not multiply by [[0 (number)|zero]]. Some generalized [[Product (mathematics)|products]], such as a [[dot product]], are never injective.
== আরও দেখুন ==
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