Is a numerical equality (like $1+2 = 3$) an algebraic equation?

In google search we have: "equation ɪˈkweɪʒ(ə)n/ noun noun: equation; plural noun: equations

a statement that the values of two mathematical expressions are equal (indicated by the sign =)."

In Wikipedia we have: "In mathematics, an equation is a statement of an equality containing one or more variables."

In Merriam-webster we have: " Definition of equation for English Language Learners

mathematics : a statement that two expressions are equal (such as $8 + 3 = 11$ or $2x – 3 = 7$)


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    $\begingroup$ It may be a matter of philosophy, but I would say that $1+2=3$ is an equation. I might even go so far as to say that it is an algebraic equation---typically, algebraic equations are those that involve polynomials, and that is an equation involving three constant polynomials. $\endgroup$ – Xander Henderson Aug 3 '17 at 19:04
  • $\begingroup$ "algebraic equation" is an equality with variables. The equality with constant numbers is an identity. An algebraic equation may also be an identity, e.g. $\sin^2x+\cos^2x=1$. $\endgroup$ – farruhota Aug 4 '17 at 8:54

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