# Is google's definition of polynomial correct?

Definition of polynomial from google's search engine dictionary:

an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

I searched on what poly means, and have got this from etymology dictionary:

word-forming element meaning "many, much, multi-, one or more,"....

And from wikipedia, monomial is

a polynomial which has only one term.

If google is right, how can monomial (having one term) be a polynomial (having greater than two terms - from the above definition)? Or is google wrong? Or is Etymology dictionary wrong?

• polynomial is a general definition , like "tree". Monomial is specific like "oak tree". an oak tree is still a tree, just like a monomial is still a polynomial – The Integrator Jun 12 '18 at 14:53
• A simple def is : "a polynomial is an expression ..." A formal def is "Let $R$ he a ring and let $R[x]$ denote the set of all sequences of elements of $R$ : $(a_0,a_1,\ldots)$ such that $a_i = 0$ for all but a finite number of indices $i$." – Mauro ALLEGRANZA Jun 12 '18 at 14:54
• I’ve always seen that $P_n(x) = \displaystyle \sum_{i=0}^n a_ix^i$ for $n\in\Bbb Z$ where $\bigcup_{i=0}^n\{a_i\}\subset\Bbb R$ or $\subset\Bbb C$, and if $n=0$ then so be it, though I can’t substantiate this. – gen-ℤ ready to perish Jun 12 '18 at 15:01

The definition I learned for polynomials definitely included monomials. It also included constants and $0$. It would be very inconvenient to exclude them because the set of polynomials would not be closed under addition. The etymology is correct, but we don't have to follow etymology exactly when we define terms. I would see the poly- prefix as reflecting the fact that there may be many terms, but not requiring them.