According to the Wikipedia and Encyclopædia Universalis, an equation must contain at least one variable but there is no such condition mentioned in other definitions.
Thus can we call the following equalities equations? Columbia Encyclopedia says yes but this contradicts with Wikipedia and Encyclopædia Universalis definitions.
$$1+1=2$$
$$9+4=13$$
In mathematics, an equation is a statement of an equality containing one or more variables. –Wikipedia
The original 2 citations mentioned in the Wikipedia article are mentioned later in this question
Equation, Statement of equality between two expressions consisting of variables and/or numbers. –Encyclopedia Britannica
An equation is a mathematical expression stating that two or more quantities are the same as one another –Wolfram Mathworld
a mathematical statement in which you show that two amounts are equal using mathematical symbols –Cambridge Dictionary
A statement that the values of two mathematical expressions are equal (indicated by the sign =) –Oxford Dictionary
Equation, in mathematics, a statement, usually written in symbols, that states the equality of two quantities or algebraic expressions, e.g., x+3=5. (…) A numerical equation is one containing only numbers, e.g., 2+3=5 –Columbia Encyclopedia, 6th ed
The Wikipedia definition cites 2 different sources. I will quote them here:
An equation is an equality between two mathematical expressions, therefore a formula of the form A=B, where the two members A and B of the equation are expressions in which one or more variables, represented by letters, appear –Encyclopædia Universalis, French-language general encyclopedia published by Encyclopædia Britannica, Inc (Translated by Google Translate, emphasis mine.)
"A statement of equality between two expressions. Equations are of two types, identities and conditional equations (or usually simply "equations")". « Equation », in Mathematics Dictionary, Glenn James [de] et Robert C. James [de] (éd.), Van Nostrand, 1968, 3 ed. 1st ed. 1948, p. 131.
So, I am still confused. The first definition of the above two definitions, says that there must be a variable and the 2nd one has no such condition.
The reason, I am asking the question because, in India, some popular textbooks have mentioned that an equation must contain a variable. Here is the definition used in the NCERT class 7 mathematics book (Page 79).
Here is another Government published book, WBBSE class 7 mathematics textbook (language: Bengali) where they instructed the students to find out which of the followings are equations and which are not. In the solutions, they didn't consider (f) and (g) as equations.
People having the idea that an equation must contain an unknown, can be found often though. For example, let's consider this similar unanswered question on this forum. There are only 2 comments and they contradict each other. Also, this question have some answers where the users believe that an equation should have an unknown.
An equation is meant to be solved, that is, there are some unknowns
You solve an equation, while you evaluate a formula.
Best Answer
The definition on Wikipedia is unusual and does not match the usual usage of the term "equation" by mathematicians. Mathematicians regularly use the term "equation" to refer to any statement that two things are equal written with the symbol $=$, regardless of whether any variables are involved. It is usually used as an informal term, but can be given precise formal definitions in various settings. I do not know of any precise formal definition that requires there to be at least one variable.