Minimal counterexample
Okay kiddo, let's say you are trying to find something out or prove something to be true. You start looking at different things and trying different stuff, but then you come across something that seems to break the rule or prove the thing you're trying to find out is not true.
Now, instead of getting frustrated and giving up, you might think "well, let me look at this thing that breaks the rule or seems to go against what I'm trying to prove. Maybe if I understand it better, I'll be able to figure out why it's not working or why it's such an exception."
When you do this, you are looking for what's called a minimal counterexample.
The word "minimal" means "the smallest or least amount possible", so a minimal counterexample is the smallest possible thing that goes against what you're trying to prove or the rule you're testing.
Instead of looking at lots of different things that might break the rule or prove the thing you're trying to find out is not true, you focus on the smallest or simplest thing that does this. By doing this, you can often figure out why the rule or thing you're trying to prove is not true, or you can find a way to change or adjust the rule so it does apply to everything else.
So, a minimal counterexample is like a little puzzle or mystery that you have to solve in order to understand something better or prove it to be true.
Now, instead of getting frustrated and giving up, you might think "well, let me look at this thing that breaks the rule or seems to go against what I'm trying to prove. Maybe if I understand it better, I'll be able to figure out why it's not working or why it's such an exception."
When you do this, you are looking for what's called a minimal counterexample.
The word "minimal" means "the smallest or least amount possible", so a minimal counterexample is the smallest possible thing that goes against what you're trying to prove or the rule you're testing.
Instead of looking at lots of different things that might break the rule or prove the thing you're trying to find out is not true, you focus on the smallest or simplest thing that does this. By doing this, you can often figure out why the rule or thing you're trying to prove is not true, or you can find a way to change or adjust the rule so it does apply to everything else.
So, a minimal counterexample is like a little puzzle or mystery that you have to solve in order to understand something better or prove it to be true.