In mathematics and logic, a direct proof is a way of showing the truth or falsehood of a given statement by a straightforward combination of established...

The book Proofs from THE BOOK, published in 2003, is devoted to presenting 32 proofs its editors find particularly pleasing. In direct proof, the conclusion...

of Euclidean division. The generalization of this proof to any degree is given below in § Direct proof. The polynomial remainder theorem follows from the...

least a version of it. A standard proof of the Poincaré lemma uses the homotopy invariance formula (cf. see the proofs below as well as Integration along...

in question holds. This is a method of direct proof. A proof by exhaustion typically contains two stages: A proof that the set of cases is exhaustive; i...

assert a proposition to constitute a proof of that proposition. For example, a signature constitutes direct proof of authorship; less directly, handwriting...

also below for the direct proofs). Bourbaki's Commutative Algebra gives a direct proof. Kaplansky's Commutative Rings includes a proof due to David Rees...

whether a "direct" proof is possible; allegedly "direct" proofs have been published, but not everyone agrees that these proofs are "direct." For example...

Death Proof is a 2007 American slasher film written and directed by Quentin Tarantino. It stars Kurt Russell as a stuntman who murders young women with...

its logically equivalent contrapositive, and an associated proof method known as § Proof by contrapositive. The contrapositive of a statement has its...

foundations of statistical mechanics.[citation needed] There is a straightforward proof of this theorem. As an introduction, recall that if two events are statistically...

61–71. K. Burns, B. Hasselblatt, "The Sharkovsky Theorem: A Natural Direct Proof" (2008). Accessed 3 February 2023. Alsedà, L.; Llibre, J.; Misiurewicz...

{d} x.} Carleman's inequality follows from the case p = 0. An elementary proof is sketched below. From the inequality of arithmetic and geometric means...

{C} } , are eigenfunctions of a linear, time-invariant operator. A simple proof illustrates this concept. Suppose the input is x ( t ) = A e s t {\displaystyle...

occurs when an individual is believed to be dead, despite the absence of direct proof of the person's death, such as the finding of remains (e.g., a corpse...

results. Some modern model checking tools produce a "proof log" detailing each step in their proof, making it possible to perform, given suitable tools...

Proof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects,...

is also a direct proof: Let R = {x1, x2, ... , xφ(n)} be a reduced residue system (mod n) and let a be any integer coprime to n. The proof hinges on the...

its original proof Mathematical induction and a proof Proof that 0.999... equals 1 Proof that 22/7 exceeds π Proof that e is irrational Proof that π is irrational...

conjugation. Zassenhaus proved this lemma specifically to give the most direct proof of the Schreier refinement theorem. The 'butterfly' becomes apparent...

Stromatoporoidea, especially in the Silurian period. Although there is no direct proof, it is inferred that these Palaeozoic corals possessed stinging cells...

alternate proof of a theorem of Lebesgue characterizing dimensionality of Euclidean spaces. It was later noticed that this lemma provides a direct proof of the...

Lacey, and Wierdl, Karl E. Petersen in 1983 published an "especially direct proof" of Cotlar's 1955 theorem. In January 1994 in Caracas, an international...

focused proofs are a family of analytic proofs that arise through goal-directed proof-search, and are a topic of study in structural proof theory and...

For a direct proof, see also the characterisation of the nilradical of a ring. This fact is also known as fourth isomorphism theorem. Proof: R = I +...

the solution may be done as in § Existence (constructive proof) or § Existence (direct proof). However, the latter construction may be simplified by using...

was the 4th generation descendant of King Naemul, which also provides direct proof that his family name was Kim. In Samguk Yusa, his name was instead recorded...

paracompact. Later Ernest Michael gave a direct proof of the latter fact and M.E. Rudin gave another, elementary, proof. a-paracompact space Paranormal space...

potential and normal matter that was claimed by Clowe et al. as "A Direct Empirical Proof of the Existence of Dark Matter" arguing that modified gravity theories...

Proof of work (also written as proof-of-work, an abbreviated PoW) is a form of cryptographic proof in which one party (the prover) proves to others (the...