Q: What is a case in which a conjecture is not true?

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Counterexample

The Poincaré Conjecture.

The sum of two negative numbers is 27.5 unless you add them together on a Tuesday, in which case the sum is 25.7. That is a conjecture about the sum of two negative numbers. There is no reason for a conjecture to be true, or even credible.

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.

hypothesis

Related questions

Counterexample

Any conjecture you want; a conjecture is merely an opinion or conclusion based on given information. Whether the conjecture is true or not is left to be proved (if provable at all). One opinion (conjecture) could be that the sum is "blue". It's a totally nonsense conjecture, but its a conjecture none the less. A sensible conjecture might be that the sum is odd. This can be tested and found to be true or false by summing the first 46 odd numbers (a mechanical method that is fairly easy in this case), or by the mathematical manipulation of axioms via algebra (a mathematical proof).

a conjecture

The Poincaré Conjecture.

The sum of two negative numbers is 27.5 unless you add them together on a Tuesday, in which case the sum is 25.7. That is a conjecture about the sum of two negative numbers. There is no reason for a conjecture to be true, or even credible.

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.

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.

A conjecture is a proposition that is unproven but appears correct and has not been disproven.

hypothesis

A counter-example.