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Transitive Property of Inequalities

Any of the following properties:

If a < b and b < c , then a < c.
If a b and b c , then a c.
If a > b and b > c , then a > c.
If a b and b c , then a c.

Note: This is a property of equality and inequalities. One must be cautious, however, when attempting to develop arguments using the transitive property in other settings.

Here is an example of an unsound application of the transitive property: "Team A defeated team B, and team B defeated team C. Therefore, team A will defeat team C."

 

 

See also

Transitive property of equality, reflexive property of equality, symmetric property of equality, inequality rules

 


  this page updated 28-jul-14
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons
NCTM Web Bytes December 2004 Web Bytes March 2005 Web Bytes