Why should the exponents of polynomials just be whole numbers

[alyafey22]

Why should the exponents of polynomials just be whole numbers ?

 

[chiro]

Why should the exponents of polynomials just be whole numbers ?

That's just the definition of a polynomial.

I think I should point out that its got a bit to do with the history of mathematics. If I remember, Descartes introduced analytical geometry and also the notation of x^n.

Most examples of functions that were analyzed dealt with low order polynomials such as quadratics and cubics.

Also another thing is that with things like Taylor series, you can approximate functions at some level of accuracy with polynomials of some degree.

But yeah to answer your question again, its just because they are defined that way.