01 Jan '13 13:312 edits

Anyone:

Correct me if I am wrong but; two of the implications of the proven Godel's theorem is that:

1, there must be some mathematical theorems that can be made that are unprovable and yet are nevertheless true.

2, we cannot ever know exactly which mathematical theorems are the ones that are both unprovable and yet are nevertheless true.

My question is this;

is the number of possible mathematical theorems that are both unprovable and yet are nevertheless true finite or infinite?

Regardless of the answer to this question, I find it interesting to note that one of the implications of 1, and 2, above is that research into general mathematics can logically never end with an ultimate climax of the gaining of complete knowledge and understanding of mathematics because that would have to include a reliable way of determine the truth or falsity of any possible mathematical theorem without exception which would be impossible. In other words, there would always be something to research in mathematics for, at the very least, there will always be a mathematical theorem ( actually an infinite number of them? -that's my question ) that may be both true and provable but have yet to be mathematically proven true and so yet to be also proven provable. This means general research in mathematics will be research without end.

Correct me if I am wrong but; two of the implications of the proven Godel's theorem is that:

1, there must be some mathematical theorems that can be made that are unprovable and yet are nevertheless true.

2, we cannot ever know exactly which mathematical theorems are the ones that are both unprovable and yet are nevertheless true.

My question is this;

is the number of possible mathematical theorems that are both unprovable and yet are nevertheless true finite or infinite?

Regardless of the answer to this question, I find it interesting to note that one of the implications of 1, and 2, above is that research into general mathematics can logically never end with an ultimate climax of the gaining of complete knowledge and understanding of mathematics because that would have to include a reliable way of determine the truth or falsity of any possible mathematical theorem without exception which would be impossible. In other words, there would always be something to research in mathematics for, at the very least, there will always be a mathematical theorem ( actually an infinite number of them? -that's my question ) that may be both true and provable but have yet to be mathematically proven true and so yet to be also proven provable. This means general research in mathematics will be research without end.