Section A.4 Examples (and how to write them)
Here’s a note about the difference between a proposition in math (versus formal logic). In math, we understand propositions (and theorems, lemmas, corollaries, etc.) to be statements that are true (and proved/provable) so that we can cite them when we need to use them. You can see the confusion that would ensue if a paper contained “Proposition 1: All even integers are prime” under that assumption, even if followed immediately by a counterexample! So, if you are showing that a statement is not true as part of a writing assignment, here’s what that might look like:
Example.
It is not the case that every even integer is prime. Notice that the integer \(8\) is even. Although \(8\) divides \(24 = (2)(12)\text{,}\) it divides neither \(2\) nor \(12\text{.}\) Therefore, by (definition of prime/proposition about prime numbers/whatever it is), \(8\) is not prime.
To break that down into more of a template:
Example.
[Topic sentence: what’s the point of this example?] [Supporting mathematical evidence, less formal than a proof, but still following the stylistic conventions of good mathematical writing!] [Concluding sentence.]
