pseudoequation

Pseudoequation is an informal term used in some scientific and mathematical writings to describe a relation that is expressed in the form of an equation but is not a rigorous or exact equality. It often denotes a heuristic, empirical, or conditionally valid relationship rather than a universal law. The prefix pseudo- signals that the statement is contingent, approximate, or assumed for modeling, rather than derived from first principles.

In practice, pseudoequations appear in several contexts. In physics and engineering, they may summarize a simplifying assumption or an effective law valid within a specified regime—for example, using an approximate constitutive relation or a phenomenological fit to data. In economics or biology, relationships between variables are sometimes written as equations to convey a trend or dependency, with explicit caveats about estimation error or limited applicability. In mathematics education or research, students may encounter pseudoequations that guide reasoning before a formal proof is established.

A key distinction is that a pseudoequation is not guaranteed to hold universally; it may be regionally valid, sample-dependent, or contingent on modeling choices. Treating a pseudoequation as an exact identity can lead to misinterpretation or error. When used, it should be accompanied by statements about assumptions, domain of validity, and uncertainty.

There is no strict formal definition, and the term is not widely standardized; writers may use it variably to flag non-rigorous or provisional expressions that resemble equations.