Why should the exponents of polynomials just be whole numbers

In summary, the exponents of polynomials are traditionally limited to whole numbers due to the historical development of mathematics and the use of polynomials for approximation and analysis of functions. This limitation is simply a definition and has been traditionally used for functions with low order polynomials.
  • #1
alyafey22
Gold Member
MHB
1,561
0
Why should the exponents of polynomials just be whole numbers ?
 
Mathematics news on Phys.org
  • #2


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.
 

1. What are the benefits of having exponents of polynomials as whole numbers?

The use of whole numbers as exponents in polynomials allows for easier computation and manipulation of expressions. It also allows for the identification of patterns and relationships between different terms in the polynomial.

2. Can polynomials have exponents that are not whole numbers?

Yes, polynomials can have exponents that are fractions or decimals. However, these types of exponents may result in complex or irrational expressions, making it more difficult to work with the polynomial.

3. Why are whole numbers considered more "convenient" for exponents?

Whole numbers are considered more convenient for exponents because they result in simpler expressions and can be easily represented in terms of repeated multiplication. This makes it easier to perform operations such as addition, subtraction, and multiplication on polynomials.

4. Are there any real-life applications where whole number exponents are used in polynomials?

Yes, whole number exponents are commonly used in real-life applications of polynomials, such as in finance, physics, and engineering. For example, the formula for compound interest uses whole number exponents to represent the number of years the interest is compounded.

5. Is there a specific reason why whole numbers are used as exponents in polynomials?

The use of whole numbers as exponents in polynomials is a convention that has been established over time due to the ease of computation and the simplicity it provides in representing and understanding polynomial expressions. It is also a result of the properties and rules of exponents that make whole numbers the most practical choice.

Similar threads

B Finding polynomials with given roots
    • General Math
Replies
14
Views
579
B Obtaining a Future Numbers Increase With Exponent From Past Increase
    • General Math
Replies
8
Views
907
B Why Is a Cubic Polynomial Called 'Third Degree'?
    • General Math
Replies
3
Views
931
Factorizing Polynomials with Irrational Exponents
    • General Math
Replies
8
Views
1K
B Super basic polynomial and exponent definition help
    • General Math
Replies
15
Views
1K
I A doubt about the multiplicity of polynomials in two variables
    • General Math
Replies
8
Views
1K
Definition of a polynomial? and degree? integral and ration
    • General Math
Replies
11
Views
2K
I Understanding Algebraic Numbers & Proving Them
    • General Math
Replies
1
Views
963
MHB Find Polynomials Fulfilling Real Coefficient Equation
    • General Math
Replies
1
Views
747
MHB Real Roots of Polynomial Minimization Problem
    • General Math
Replies
1
Views
748

Hot Threads

Recent Insights

Back
Top