数学中的伯努利不等式是说：对任意整数，和任意实数，

如果且是偶数，则不等式对任意实数成立。

可以看到在，或时等号成立，而对任意正整数和任意实数，，有严格不等式：

伯努利不等式经常用作证明其他不等式的关键步骤。

In real analysis, Bernoulli's inequality (named after Jacob Bernoulli) is an inequality that approximates exponentiations of 1 + x.

The inequality states that

for every integer r ≥ 0 and every real number x ≥ −1. If the exponent r is even, then the inequality is valid for all real numbers x. The strict version of the inequality reads