Category:Existence and Uniqueness of Positive Root of Positive Real Number
This category contains pages concerning Existence and Uniqueness of Positive Root of Positive Real Number:
Let $x \in \R$ be a real number such that $x \ge 0$.
Let $n \in \Z$ be an integer such that $n \ne 0$.
Then there always exists a unique $y \in \R: \paren {y \ge 0} \land \paren {y^n = x}$.
Hence the justification for the terminology the positive $n$th root of $x$ and the notation $x^{1/n}$.
Positive Exponent
Let $x \in \R$ be a real number such that $x \ge 0$.
Let $n \in \Z$ be an integer such that $n > 0$.
Then there always exists a unique $y \in \R: \paren {y \ge 0} \land \paren {y^n = x}$.
Negative Exponent
Let $x \in \R$ be a real number such that $x \ge 0$.
Let $n \in \Z$ be an integer such that $n < 0$.
Then there always exists a unique $y \in \R: \paren {y \ge 0} \land \paren {y^n = x}$.
Subcategories
This category has the following 2 subcategories, out of 2 total.
Pages in category "Existence and Uniqueness of Positive Root of Positive Real Number"
The following 4 pages are in this category, out of 4 total.