Diagonal argument information

A diagonal argument, in mathematics, is a technique employed in the proofs of the following theorems: Cantor's diagonal argument (the earliest) Cantor's...

construction of a diagonal matrix (with nonzero entries only on the main diagonal) that is similar to a given matrix Diagonal argument (disambiguation)...

similar argument, N has cardinality strictly less than the cardinality of the set R of all real numbers. For proofs, see Cantor's diagonal argument or Cantor's...

used an argument with nested intervals, but in an 1891 paper, he proved the same result using his ingenious and much simpler diagonal argument. The new...

subsequently made further important contributions, including his diagonal argument and theorem. However, he never again attained the high level of his...

the set R of all real numbers; Cantor's diagonal argument shows that this set is uncountable. The diagonalization proof technique can also be used to show...

different infinities. The inequality was later stated more simply in his diagonal argument in 1891. Cantor defined cardinality in terms of bijective functions:...

argument in different terms is given in [Raatikainen (2015a)].) The lemma is called "diagonal" because it bears some resemblance to Cantor's diagonal...

An argument is a series of sentences, statements, or propositions some of which are called premises and one is the conclusion. The purpose of an argument...

In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices...

real numbers (see Cantor's first uncountability proof and Cantor's diagonal argument). His proofs, however, give no indication of the extent to which the...

{\displaystyle A\subseteq B} by applying a proof technique known as the element argument: Let sets A and B be given. To prove that A ⊆ B , {\displaystyle A\subseteq...

the set of all functions from Y to X and |XY| = |X||Y|. Cantor's diagonal argument shows that the power set of a set (whether infinite or not) always...

In mathematics, an argument of a function is a value provided to obtain the function's result. It is also called an independent variable. For example,...

In logic and deductive reasoning, an argument is sound if it is both valid in form and has no false premises. Soundness has a related meaning in mathematical...

problem NP-completeness of the Boolean satisfiability problem Cantor's diagonal argument set is smaller than its power set uncountability of the real numbers...

it is uncountable. For an elaboration of this result see Cantor's diagonal argument. The set of real numbers is uncountable, and so is the set of all...

be used to state and prove impossibility results akin to Cantor's diagonal argument, Gödel's incompleteness theorem, and Turing's halting problem. In...

showing that this implies different sizes of infinity, per Cantor's diagonal argument. This led to the controversy over Cantor's set theory. In the same...

most countably many definable real numbers. However, by Cantor's diagonal argument, there are uncountably many real numbers, so almost every real number...

term "diagonal argument" is sometimes used to refer to this type of enumeration, but it is not directly related to Cantor's diagonal argument.[citation...

συλλογισμός, syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two...