A counter-example.
hypothesis
Counterexample
My conjecture is that the sum is 67. A conjecture does not have to be true, or even plausible. You should be able to test it. If it is found to be true then in is no longer a conjecture, if it is found to be false, it is rejected - and so no longer a conjecture. If it cannot be proved either way, it remains a conjecture.
Counterexample
A counter-example.
hypothesis
Counterexample
a conjecture
To be true a Conjecture must be true for all cases.
Because that is what a conjecture is! It is a proposition that has to be checked out to see f it isalways true, false or indeterminate,sometimes true, false or indeterminate,never true, false or indeterminate.Once its nature has been decided then it is no longer a conjecture.
My conjecture is that the sum is 67. A conjecture does not have to be true, or even plausible. You should be able to test it. If it is found to be true then in is no longer a conjecture, if it is found to be false, it is rejected - and so no longer a conjecture. If it cannot be proved either way, it remains a conjecture.
Counterexample
It is a proposition that is believed to be true but has not [yet] been proven to be true. Clearly, if proven to be false it would no longer be a conjecture.
Counter Example
A counter example is a statement that shows conjecture is false.
A counterexample.