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. (Click here for the transitive property of equality.) 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
