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The universality of an algorithm is usually proven by analyzing proteins with low sequence identity to those in the learning set.
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And since politicians and policymakers almost inevitably overstep, the skeptic is usually proved correct — eventually.
The independence of the axioms is usually proved by using more than two truth values.
Combinatorial completeness is usually proved via defining a "pseudo" λ-abstraction (or bracket abstraction) in CL.
In practice, correctness of algorithms in computational geometry is usually proved using the unrealistic Real RAM machine model of computation, which allows comparison of real numbers, with the undesirable result that correct algorithms, when implemented, turn into unreliable programs.
The present authors strongly believe that these ideas will clearly influence on the further development of Hardy type inequalities and that these ideas and proofs will be used in analysis books in the future (in almost all such books even the classical Hardy inequality (1.1) is usually proved by using essentially his original proof via partial integration and Pólya's simplification).
But one or two of Saxo's punts are usually proved right, or half-right.
The line between cheerleader and journalist can be thin amongst their corps – most were wearing their country's colours of black, green and gold – but when they promise that Bolt is in form they are usually proved right.
In the case of cone metric spaces, fixed point results are usually proved under assumption that the cone is normal.
Although, for expository reasons, our results will be usually proved only for uniformly convex metric spaces with a monotone modulus of convexity, they also hold when there is a lower semicontinuous modulus of convexity.
Even after the fact, economists agree, it is usually impossible to prove which policies led to economic strengthening and which caused deterioration.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com