Difference between revisions of "Strict inequality"
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A strict [[inequality]] is an inequality where the [[inequality symbol]] is either <math> > </math> (greater than) or <math> < </math> (less than). That is, a strict inequality is an inequality which has no [[equality condition]]s. | A strict [[inequality]] is an inequality where the [[inequality symbol]] is either <math> > </math> (greater than) or <math> < </math> (less than). That is, a strict inequality is an inequality which has no [[equality condition]]s. | ||
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| + | For example: <math>x>1</math> ''is'' a strict inequality. However, <math>x\geq1</math> is ''not'' a strict inequality. | ||
An example of a well-known strict inequality is the [[Triangle Inequality]], which states that, in a [[nondegenerate]] triangle <math>ABC</math>, the following relation holds: | An example of a well-known strict inequality is the [[Triangle Inequality]], which states that, in a [[nondegenerate]] triangle <math>ABC</math>, the following relation holds: | ||
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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>. | + | 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>. |
Latest revision as of 10:53, 2 September 2020
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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: 
is a strict inequality. However, 
is not a strict inequality.
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 
, 
.
