Why should the exponents of polynomials just be whole numbers

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SUMMARY

Exponents of polynomials are defined strictly as whole numbers due to historical conventions established in mathematics, notably by René Descartes, who introduced analytical geometry and the notation of x^n. The focus on low-order polynomials, such as quadratics and cubics, has shaped this definition. Additionally, polynomials are utilized in Taylor series to approximate functions with a certain degree of accuracy, reinforcing the importance of whole number exponents in polynomial functions.

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alyafey22
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Why should the exponents of polynomials just be whole numbers ?
 
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alyafey22 said:
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.
 

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