New answers tagged concept-motivation
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When I was thinking about a similar question, I found the article "What is an equation" by S. Marcus and S.M. Watt ( https://www.academia.edu/3287674/What_is_an_Equation ) As far as I understand they discuss the difference between "equation" and "equality" in some languages. In some language (like english) there is no difference,...
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As pointed out by @AmyB and @DanielRCollins, an equation is simply a statement that two expressions are equal.
@Adam remarks that the equation-identity distinction doesn't seem useful; on the contrary, it is instructive to distinguish an identity from a mere equation:
Let $z\in\mathbb C,$ $\;C_n$ denote $\left(z^2-2z\cos\left(\frac{n\pi}9\right)+1\right),$ ...
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