Proof of impossibility
Have you ever heard someone say that something is impossible? Like if you try to jump over a tall building or if you try to turn a carrot into a computer, it's just impossible? Well, sometimes people want to prove that things are impossible for real, and they use something called "proof of impossibility."
Say you have a problem that needs solving, like how to fit a bunch of different shapes into a puzzle. You might try really hard to find a solution, but no matter how hard you try, you just can't figure it out. That's when you might start to think that it's impossible to do. But how do you know for sure?
Proof of impossibility is a way to show that something is impossible to do or impossible to exist. It's like a really strong argument that can't be refuted. To do this, you need to use logic and math to show that there's no possible way for the thing you're trying to do to happen.
Let's go back to our puzzle example. Say you've tried every possible combination of the pieces, but you just can't get them to fit together. How can you prove that it's impossible to solve the puzzle? Well, you might use something called "reductio ad absurdum," which is Latin for "reduction to absurdity."
This means that you assume the opposite of what you want to prove, and then show that it leads to a contradiction or an absurdity. So, in our puzzle example, we might assume that there IS a way to solve the puzzle, even though we haven't found it yet. Then, we would try to show that this assumption leads to something that just can't be true. Maybe we find that if the puzzle can be solved, then 1 + 1 = 3, which is impossible.
Once we've shown that our assumption leads to something impossible, we can conclude that our original assumption was wrong, and therefore the puzzle is impossible to solve. This is proof of impossibility!
So, to sum up, proof of impossibility is a way to show that something is impossible using logic and math. It's like a really strong argument that can't be refuted, and it often involves assuming the opposite of what you want to prove and showing that it leads to something impossible or absurd.
Say you have a problem that needs solving, like how to fit a bunch of different shapes into a puzzle. You might try really hard to find a solution, but no matter how hard you try, you just can't figure it out. That's when you might start to think that it's impossible to do. But how do you know for sure?
Proof of impossibility is a way to show that something is impossible to do or impossible to exist. It's like a really strong argument that can't be refuted. To do this, you need to use logic and math to show that there's no possible way for the thing you're trying to do to happen.
Let's go back to our puzzle example. Say you've tried every possible combination of the pieces, but you just can't get them to fit together. How can you prove that it's impossible to solve the puzzle? Well, you might use something called "reductio ad absurdum," which is Latin for "reduction to absurdity."
This means that you assume the opposite of what you want to prove, and then show that it leads to a contradiction or an absurdity. So, in our puzzle example, we might assume that there IS a way to solve the puzzle, even though we haven't found it yet. Then, we would try to show that this assumption leads to something that just can't be true. Maybe we find that if the puzzle can be solved, then 1 + 1 = 3, which is impossible.
Once we've shown that our assumption leads to something impossible, we can conclude that our original assumption was wrong, and therefore the puzzle is impossible to solve. This is proof of impossibility!
So, to sum up, proof of impossibility is a way to show that something is impossible using logic and math. It's like a really strong argument that can't be refuted, and it often involves assuming the opposite of what you want to prove and showing that it leads to something impossible or absurd.
Related topics others have asked about: