a conjecture
The Perpendicular bisector concurrency conjecture is the circumcenter
My conjecture (an opinion based on incomplete information) is that the product of two odd numbers is 22. There is no requirement for a conjecture to be true.
theorem
Counter-example
Hypothesis
It is a hypothesis.
homosteis
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).
The future tense of "conjecture" is "will conjecture."
a conjecture is disproved if it is shown to be false. this can be done by providing a single concrete example (e.g. with actual numbers, functions, etc) that shows the conjecture's premise does not necessarily lead to its conclusion. alternatively, a conjecture could be shown to be false (i.e. disproved) by demonstrating that IF it were true then a logical consequence would be a clearly wrong statement (e.g. 2 + 2 =5)
a conjecture
The Poincaré Conjecture.
A conjecture should be testable. You test it and if it fails the test, it is a false conjecture.
Th3 variabl3
One possible conjecture is that their sum is 27. The conjecture is patently false, but that does not stop it being 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.