Definition:Root (Analysis)

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Root (Analysis) may refer to:

Root of Number

Let $x, y \in \R_{\ge 0}$ be positive real numbers.

Let $n \in \Z$ be an integer such that $n \ne 0$.


Then $y$ is the positive $n$th root of $x$ if and only if:

$y^n = x$

and we write:

$y = \sqrt[n] x$


Using the power notation, this can also be written:

$y = x^{1/n}$


Root of Equation

Let $\map E x$ be a mathematical expression representing an equation which is dependent upon a variable $x$.

A root of $\map E x$ is a constant which, when substituted for $x$ in $\map E x$, makes $\map E x$ a true statement.


Root of Function

Let $f: R \to R$ be a mapping on a ring $R$.

Let $x \in R$.


Then the values of $x$ for which $\map f x = 0_R$ are known as the roots of the mapping $f$.