Difference between revisions of "Strict inequality"
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| − | 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>. | + | 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 10:42, 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 
, the following relation holds:
A non-example is the Trivial Inequality which states that if 
is a real number then 
. This inequality is not strict because it has an equality case: when 
, 
.
