SmallestCounterExample.md (613B)
1 # Smallest Counterexample 2 3 Abstract Math 10.3. This is similar to [Induction](Induction.md) and [[StrongInduction.md]] 4 5 **Definition:** Assume that the first element of a series is true and that not all other elements of the series are also true. We find the first element that is untrue denoted as $S_k$ and show that $S_{k-1}$ being true and $S_k$ being untrue is contradictory. 6 7 **Steps:** 8 1. Check that first statement $S_1$ is true 9 2. Suppose not every statement $S_n$ is true 10 3. Let k > 1 be the first instance where $S_k$ is false 11 4. Show that $S_{k-1}$ being true and $S_k$ being false are contradictory 12