Transitive Property of Inequalities

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."