Definition:Rational Function
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Definition
Let $P: \R \to \R$ and $Q: \R \to \R$ be polynomial functions on the set of real numbers.
Let $S$ be the set $\R$ from which all the roots of $Q$ have been removed.
That is, $S = \R - \left\{{x \in \R: Q \left({x}\right) = 0}\right\}$.
Then the equation $y = \dfrac {P \left({x}\right)} {Q \left({x}\right)}$ defines a function from $S$ to $\R$.
Such a function is called a rational function.
Expand to include polynomial functions on the general field.
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Sources
- C.R.J. Clapham: Introduction to Abstract Algebra (1969)... (previous)... (next): $\S 4.17$: Example $26$
- K.G. Binmore: Mathematical Analysis: A Straightforward Approach (1977)... (previous)... (next): $\S 7.6$
