Common Errors in Proofs

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(Discussion of these and other common errors are on pages 155-158 of your textbook.)

Arguing from Examples--scoring code AfE--sample AfE errors.

What-to-Show and What-You-Know Confusion--scoring code KandS--sample KandS errors.

Unjustified Assertion--scoring code UA--sample UA errors.

Jumping to a Conclusion--scoring code J2C--sample J2C errors.

Same Letter Error--scoring code SLE--sample SLE errors.

Improper Negation of a Conditional--The proper negation of a condition:
~(if P then Q) is equivalent to (P and ~Q). The negation of a conditional is NOT another conditional.

Making Stuff Up--The concept of proof in mathematics requires that you only use definitions and theorems that have already been accepted. To all of a sudden assert something like "If an integer is not divisible by 2 or 3 then it is prime" or "all repeating decimals are rational" is unacceptable whether or not the assertion is true. This might be considered a severe version of a UA error.

Unjustified Steps--Each step of your proof is supposed to have a justification.