For any positive integer
, the function
is continuous and strictly increasing on
. Moreover
and
. Therefore
is a bijection from
onto itself. It is invertible and its inverse
is called the
root function.
We denote:
Remark 5.7.3
We give here a definition of roots valid only for non negative numbers. Many pocket calculators compute roots for
negative numbers; in fact their ``definition'' of roots is different from what we explain here, and coincides with
ours for non negative numbers.
We can now define rational powers of a non negative real number:
Definition 5.7.5
let
be a rational number; we denote it in reduced form
, where
is an integer and
is a positive integer. Then
.
For example:
.
Properties 5.7.6

.

.
For example:
.
Noah DanaPicard
20071228