Strict inequality

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A strict inequality is an inequality where the inequality symbol is either $>$ (greater than) or $<$ (less than). That is, a strict inequality is an inequality which has no equality conditions.

For example: $x>1$ is a strict inequality. However, $x\geq1$ is not a strict inequality.

An example of a well-known strict inequality is the Triangle Inequality, which states that, in a nondegenerate triangle $ABC$, the following relation holds:


A non-example is the Trivial Inequality which states that if $x$ is a real number then $x^2 \geq 0$. This inequality is not strict because it has an equality case: when $x = 0$, $x^2 = 0$.