Sentence examples for proof establishes from inspiring English sources

An indirect proof establishes its conclusion by showing the impossibility of its opposite.

If successful, this proof establishes that there is a first mover of all moved movers which is not itself material.

The proof establishes the equivalence of the cb-norm distance and the Bures distance for completely positive maps.

The Peres proof establishes the KS result in full strength, with great simplicity, and, moreover, in an intuitively accessible way, since it operates in three dimensions; we refer the reader to Peres (1995: 197 99).

Remark 44 Obviously, the map ι from the previous proof establishes an isomorphism i h ( k ) ↦ i ∑ p, q = 1 d A p q ( k ) ( f p † f q − δ p q 1 2 ) from the algebra 〈 i h ( 1 ), …, i h 〉 Lie to the algebra 〈 i A ( 1 ), …, i A 〉 Lie for any set { A ( 1 ), …, A } of d × d Hermitian matrices.

Euclid's proof established that there will always be primes, but it says nothing about how far apart any two might be.

This proof established that the classical Greek construction problem of squaring the circle (constructing a square with an area equal to that of a given circle) by compass and straightedge is insoluble.

They include reversing the burden of proof; establishing a tribunal that would take the financial sting out of libel; preventing large and medium-sized corporations from suing; protecting service providers from the chilling effect of takedown notices; and stemming the tide of libel tourism.

Thus, when a different proof arose later on using Montel's idea of normal families, this proof established itself as standard [2].

Indeed, Hilbert saw that something stronger is true: not only does a consistency proof establish truth of real formulas provable by ideal methods, but it yields finitary proofs of finitary general propositions if the corresponding free-variable formula is derivable by ideal methods (1928, 474).

In the absence of proof establishing some other date, the one appearing in the printed or electronic matter must be accepted as correct.