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>.
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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>.

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: $x>1$ 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:

$AB+BC>AC$

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 $x = 0$, $x^2 = 0$.

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