Soundness (interactive proof)

Soundness in interactive proof is like playing with blocks. When you play with blocks, you have to make sure that they fit together properly, or else your tower will fall down. Similarly, in interactive proof, we have to make sure that the proofs that we give match up with the correct answer, or else the proof will be "unsound."

When we prove something in interactive proof, it's like we're building a tower out of blocks. We start with a hypothesis or a statement that we want to prove. Then, we use a bunch of smaller statements, or "blocks," to build up to our final proof.

However, just like with blocks, we have to make sure that our proof is built correctly or else it won't work. When we're done building our proof, we have to test it to make sure it is sound. This means that we have to check that it is indeed true.

In interactive proof, we use something called a "verifier" to check if our proof is sound. The verifier is like a teacher who checks your homework to make sure you did it correctly. The verifier will ask you questions, and you have to answer them using your proof.

The verifier will try to find any holes in your proof, like a missing block in your tower. If the verifier can find a hole in your proof, then it is unsound. This means that the proof is not correct, and we have to try again.

Overall, soundness in interactive proof is like building a tower out of blocks and making sure it is solid. The verifier checks if our proof is sound, just like a teacher checks if our homework is correct. By making sure our proofs are sound, we can be confident that they are true.