Errors and Mistakes in Developing Proofs
Learn about common mistakes in proofs.
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Common mistakes
As humans, we all make mistakes. To avoid typographic errors, we must proofread the script we write. We must carefully verify each algebraic manipulation in proof to ensure correctness. Overall, the proof must be a valid argument type, and every deduction must be according to inference rules. Sometimes, errors in algebraic manipulation are straightforward to catch, but sometimes they are very subtle. Let’s look at the following example of a wrong derivation with a subtle mistake:
We notice that every step is fine except the fifth step if we look closely. As , we can not cancel out from both sides because it equals zero. Such mistakes can lead to inconsistent results, as in line number seven.
Now let’s look at some common mistakes of argument.
The fallacy of affirming the conclusion
Let’s assume we have is true for some propositions and for a given domain. Instead of assuming true, we assume that is true for some element of the domain. The fallacy of affirming the conclusion is a wrong argument type as follows:
Let’s look at a few examples to clarify this error.
Example
Assume the domain set contains all the mammals.
Consider the following propositions:
- : is a cow.
- : is a mammal.
Assume the following statement as a fact:
The above statement is saying that every cow is a mammal. Now, let’s look at the wrong argument.
As Frankie is a mammal, therefore, Frankie is a cow.
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