The theorem is named after Felix Bernstein and Ernst Schröder. It is also known as the Cantor–Bernstein theorem or Cantor–Schröder–Bernstein theorem, after...

each other). The name Schröder–Bernstein (or Cantor–Schröder–Bernstein, or Cantor–Bernstein) property is in analogy to the theorem of the same name (from...

Schröder–Bernstein may refer to: the Schröder–Bernstein theorem in set theory Schröder–Bernstein theorem for measurable spaces Schröder–Bernstein theorems...

Cantor–Bernstein–Schroeder theorem of set theory has a counterpart for measurable spaces, sometimes called the Borel Schroeder–Bernstein theorem, since...

Felix Bernstein (24 February 1878 – 3 December 1956), was a German mathematician known for proving in 1896 the Schröder–Bernstein theorem, a central result...

The Schröder–Bernstein theorem from set theory has analogs in the context operator algebras. This article discusses such operator-algebraic results. Suppose...

same notion of computability on a set. It is reminiscent of the Schröder–Bernstein theorem in set theory and has been called a constructive version of it...

impossible by Alonzo Church and Alan Turing in 1936. By the completeness theorem of first-order logic, a statement is universally valid if and only if it...

Vorlesungen. Schröder's equation Schröder number Schröder–Bernstein property Schröder–Bernstein theorem for measurable spaces Schröder–Hipparchus number...

mapped onto N {\displaystyle {\mathbb {N} }} . Classically, the Schröder–Bernstein theorem is valid and says that any two sets which are in the injective...

Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability...

Y and Y ≤* X together imply that |Y| = |X|, a variant of the Schröder–Bernstein theorem. The composition of surjective functions is always surjective:...

Cantor–Bernstein–Schröder theorem (set theory, cardinal numbers) Cantor's theorem (set theory, Cantor's diagonal argument) Church–Rosser theorem (lambda...

bijective; its inverse is the positive square root function. By Schröder–Bernstein theorem, given any two sets X and Y, and two injective functions f: X...

than a bijection, but this issue can be repaired by using the Schröder–Bernstein theorem. Sagan, Hans (1994), Space-filling curves, Universitext, New York:...

inferential steps and often use various rules of inference to establish the theorem they intend to demonstrate. Rules of inference are definitory rules—rules...

must leave out at least one map T → Y {\displaystyle T\to Y} . Schröder–Bernstein theorem Cantor's first uncountability proof Controversy over Cantor's...

general Peirce–Schröder calculus of relatives (relation algebra with quantifiers). He also used the now antiquated notations of Ernst Schröder. For a summary...

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories...

partition P of a set S is less than or equal to S in size. Converse Schröder–Bernstein theorem: if two sets have surjections to each other, they are equinumerous...

proved results that cast new light on the problem. Some feel that Gödel's theorems give a negative solution to the problem, while others consider Gentzen's...

In mathematics, Richardson's theorem establishes the undecidability of the equality of real numbers defined by expressions involving integers, π, ln 2...

also known as a "helping theorem" or an "auxiliary theorem". In many cases, a lemma derives its importance from the theorem it aims to prove; however...

compactness theorem states that a set of first-order sentences has a model if and only if every finite subset of it has a model. This theorem is an important...

are quite similar. In fact, a weaker form of the First Incompleteness Theorem is an easy consequence of the undecidability of the halting problem. This...

This is denoted | S | ≤ | T | . {\displaystyle |S|\leq |T|.} Schröder–Bernstein theorem implies that | S | ≤ | T | {\displaystyle |S|\leq |T|} and | T...

limitations": ...the magnitudes involved should lead one to suspect that theorems and arguments based chiefly on the mere finiteness [of] the state diagram...

power set must be larger than the original set). In particular, Cantor's theorem shows that the power set of a countably infinite set is uncountably infinite...

Tarski's undefinability theorem, stated and proved by Alfred Tarski in 1933, is an important limitative result in mathematical logic, the foundations...

results were contained in earlier work of Skolem. Informally, a soundness theorem for a deductive system expresses that all provable sentences are true....