Definition:Conjugate Exponents
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Definition
Let $p, q \in \R_{\ge 1}$.
Then $p$ and $q$ are conjugate exponents if and only if:
- $\dfrac 1 p + \dfrac 1 q = 1$
General Definition
Let $\set {p_1, p_2, \ldots, p_n}$ be such that:
- $\forall i \in \set {1, 2, \ldots, n}: p_i \in \R_{\ge 1}$
Then $\left\{{p_1, p_2, \ldots, p_n}\right\}$ are conjugate exponents if and only if:
- $\ds \frac 1 {p_1} + \frac 1 {p_2} + \cdots + \frac 1 {p_n} = \sum_{i \mathop = 1}^n \frac 1 {p_i} = 1$