A conjecture is a proposed mathematical statement that has not yet been proven to be true or false.
A conjecture is considered stronger than another if it can be used to prove a larger number of statements or if it is more general than the other conjecture.
One way to prove that one conjecture is stronger than another is to show that the stronger conjecture implies the weaker one. This means that if the stronger conjecture is true, then the weaker one must also be true.
Yes, it is possible for a conjecture to be proven to be stronger than another without being proven true. This is because a conjecture can still be considered stronger if it can be used to prove a larger number of statements, even if it has not been proven to be true.
The significance of one conjecture being stronger than another is that it allows for more efficient and powerful methods of proving mathematical statements. By using a stronger conjecture, we can prove a larger number of statements and potentially make more significant advancements in mathematics.