1. Lesson 4

1.6. Lesson 4 Summary

Mathematics 20-2 M2 Lesson 4

Module 2: Logic and Geometry

 

This is a cartoon of two men standing at a chalkboard. In the middle of a proof, the words “THEN A MIRACLE OCCURS” are written. One man says to the other, “I think you should be more explicit here in step two.”

Sidney Harris/ScienceCatoonsPlus.com

Lesson 4 Summary
 

In this lesson you discovered that not all proofs are valid. A proof can be invalidated by a single error in reasoning. That error may be the result of division by zero somewhere in the proof. The use of circular reasoning or another type of error in logic also results in an invalid proof. For instance, when reasoning relies on stereotypes, the conclusions are not valid. Stereotypes are generalizations and there are always counterexamples to stereotypes.

 

An error in a proof is similar to a counterexample in that it only takes one error to invalidate the conclusion. For example, a proof that is based on a false premise is invalid, even if the argument used is valid.

 

In Lesson 5 you will apply what you have learned about reasoning to solve problems.