  A new inequality, $(x)^{p}+(1-x)^{\frac{1}{p}}\leq1$ for $p \geq 1$ and
$\frac{1}{2} \geq x \geq 0$ is found and proved. The inequality looks elegant
as it integrates two number pairs ($x$ and $1-x$, $p$ and $\frac{1}{p}$) whose
summation and product are one. Its right hand side, $1$, is the strict upper
bound of the left hand side. The equality cannot be categorized into any known
type of inequalities such as H\"{o}lder, Minkowski etc. In proving it,
transcendental equations have been met with, so some novel techniques have been
built to get over the difficulty.
