If you've got a theory that you're trying to prove, and you uncover a conclusive piece of evidence, then the case is closed. Conclusive means you've got your answer, you've proved your theory, and there can't be any doubt about it.
If want to prove that frogs can speak, and you record a frog reciting "The Midnight Ride of Paul Revere," that would be conclusive evidence for your claim. But if the frog mumbled and might have been just making frog noises, critics would say that your video is not conclusive. You can also use the word conclusive to describe winning something easily or by a large margin, like when the judges handed the tap-dancing bear a conclusive victory, and he moved on triumphantly to the finals.
adj forming an end or termination; especially putting an end to doubt or question
supplying or being a final or conclusive settlement
determining or having the power to determine an outcome
not conclusive; not putting an end to doubt or question
uncertain as a sign or indication
not leading to a definite ending or result
head-to-head, neck and neck, nip and tuck
inconclusive as to outcome; close or just even in a race or comparison or competition
not final or absolute
not definitely settling something
not precisely determined or established; not fixed or known in advance
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