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To write an indirect proof, you must prove something by finding contradictions of the negation (opposite) of what you need to prove.
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"You lied to us," one player shouted at Bloom, finding contradiction in the president's publicly stated commitment to revive football three seasons ago.
Since contradictions raised by peers seemed to have a greater weight than those raised by patients, finding contradiction among peers even though the clinician successfully refuted them, frequently led to a suspension of the final decision.
Thus, biologists are finding these contradictions very difficult to interpret.
For biologists, models that can systematize diverse sets of hypotheses to test whether they stand up to scrutiny can be invaluable for finding subtle contradictions and can point to which specific hypotheses need revision.
To obtain the lower estimate, assume for finding a contradiction that there exists a sequence ({varphi_{M_{j}}, psi_{N_{j}}}) such that ((varphi_{M_{j}})_{s}(0,0 rightarrow0).
Another young man began repeating verbatim the "nothingness" argument, as if finding no contradiction with his earlier avowed dedication to serve Christ.
As I said, whenever looking for easy answers to the Tea Party, mostly what you wind up finding is contradiction, on a state-by-state level, mostly due to the Tea Partiers' inherent decentralized nature.
It seems that in a land of contradictions, finding answers to all your questions might be a fruitless exercise.
Can Europe, as Camus had hoped, once again prove it's capable of finding energy in its contradictions and differences and, under pressure, reinvent itself as a place the whole world respects?
Working out apparent contradictions, reconciling irreconcilables, finding balances, living with paradox — these are the intellectual bread and butter of Obama's politics.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com