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I want to solve this question but I don't understand what "height" of an algebraic equation is:

Find the number of solutions of the set of all algebraic equations of height 2.

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Where did the question come from? If from a text, there should be a definition. And what set do the variables and constants in your equation come from? If it is $\mathbb{R}$, even linear equations have continuum many solutions. – Ross Millikan Oct 8 '11 at 3:30
Googling "height of an algebraic equation" finds a few references to a definition by Cantor: the sum of the absolute values of the coefficients plus the degree minus 1. There's also height of a polynomial, which is similar but different. – lhf Oct 8 '11 at 3:42
@lhf's suggestion fits well with the question here. This definition is commonly part of an argument that there are countably many algebraic numbers. – Henning Makholm Oct 8 '11 at 3:44
Agree with Henning. For the purposes of enumerating algebraic numbers it is essential that there are only finitely many algebraic equations of a given height. The height of a polynomial fails in that score even though it is useful in other contexts. – Jyrki Lahtonen Jul 8 at 14:57

You can find it in Rudin, Principles of Mathematical Analysis, page 43, problem 2, the sum of the absolute values given there is called the height of an algebraic equation.

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