Difference between revisions of "Strict inequality"

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<center><math> AB+BC>AC </math></center>
 
<center><math> AB+BC>AC </math></center>
  
A non-example is the [[Trivial Inequality]] which states that if <math>x</math> is a [[real number]] then <math>x^2 \geq 0</math>.  This inequality is not strict because it has an equality case: when <math>x = 0</math>, <math>x^2 = 0</math>.
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A non-example is the [[Trivial Inequality]] which states that if <math>x</math> is a [[real number]] then <math>\displaystyle x^2 \geq 0</math>.  This inequality is not strict because it has an equality case: when <math>x = 0</math>, <math> x^2 = 0</math>.

Revision as of 09:42, 14 August 2006

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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.

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

$AB+BC>AC$

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

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