Building a Simple Proof with a Tree
Truth trees work by creating a contradiction. We take a statement that we want to prove true, turn it around by negating it, and then show that that negation leads to contradictions.
For example, I can use this basic method to prove that there isn’t a largest even number, N:
Example: Prove there is no such thing as a largest even number, N.
-
We’ll start by inverting the fact to prove, and then we’ll show that it leads to a contradiction. Suppose that there is a largest even number, N.
-
Since N is the largest even number, then for every other even number n, n < N.
-
N is a natural number; therefore, it can be added with other natural numbers.
-
If we add 2 to N, the result will be even and it will be larger ...
Get Good Math now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
