In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of unintuitive properties. It was discovered in 1874...

In mathematics, the Smith–Volterra–Cantor set (SVC), ε-Cantor set, or fat Cantor set is an example of a set of points on the real line that is nowhere...

played a pivotal role in the creation of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one...

mathematics, a Cantor space, named for Georg Cantor, is a topological abstraction of the classical Cantor set: a topological space is a Cantor space if it...

In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous. It is a notorious counterexample in...

Cantor's first set theory article contains Georg Cantor's first theorems of transfinite set theory, which studies infinite sets and their properties....

In set theory, Cantor's diagonal argument, also called the diagonalisation argument, the diagonal slash argument, the anti-diagonal argument, the diagonal...

uncountable set X is a subset of set Y, then Y is uncountable. The best known example of an uncountable set is the set R of all real numbers; Cantor's diagonal...

that, in 1883, Georg Cantor, who attended lectures by Weierstrass, published examples of subsets of the real line known as Cantor sets, which had unusual...

when considered as subsets of the real numbers. The Cantor set is an example of an uncountable null set.[further explanation needed] Suppose A {\displaystyle...

Julia set is a Cantor space: in this case it is sometimes referred to as Fatou dust. In many cases, the Julia set of c looks like the Mandelbrot set in sufficiently...

theory of infinite sets was first developed by Georg Cantor. Although this work has become a thoroughly standard fixture of classical set theory, it has been...

curve. It is a three-dimensional generalization of the one-dimensional Cantor set and two-dimensional Sierpinski carpet. It was first described by Karl...

}{\frac {b_{n}}{3^{n+1}}}} gives the Cantor function, as conventionally defined. This is one reason why the set { H , T } N {\displaystyle \{H,T\}^{\mathbb...

first-order set theory. The term naive set theory is still today also used in some literature to refer to the set theories studied by Frege and Cantor, rather...

needed] A Cantor space is a topological space 2 N {\displaystyle 2^{\mathbb {N} }} homeomorphic to the Cantor set, whose general set is a closed set consisting...

measure of the set of algebraic numbers is 0, even though the set is dense in R {\displaystyle \mathbb {R} } . The Cantor set and the set of Liouville numbers...

meaning. The support of the Cantor distribution is the Cantor set, itself the intersection of the (countably infinitely many) sets: C 0 = [ 0 , 1 ] C 1 = [...

considering the more general concept of restricted partial quotients. The Cantor set is a set C of measure zero from which a complete interval of real numbers...

{R} } ) and a meagre subset of R . {\displaystyle \mathbb {R} .} The Cantor set is nowhere dense in R {\displaystyle \mathbb {R} } and hence meagre in...

In mathematical set theory, Cantor's theorem is a fundamental result which states that, for any set A {\displaystyle A} , the set of all subsets of...

Cantor set is uncountably infinite, but has Lebesgue measure zero. So almost all real numbers in (0, 1) are members of the complement of the Cantor set...

0 , 1 ] {\displaystyle [0,\,1]} . (The restriction of the Cantor function to the Cantor set is an example of such a function.) From it, we get a continuous...

and are called clopen sets. The ray [ 1 , + ∞ ) {\displaystyle [1,+\infty )} is closed. The Cantor set is an unusual closed set in the sense that it consists...

Riemann-integrable. The function is defined by making use of the Smith–Volterra–Cantor set and "copies" of the function defined by f ( x ) = x 2 sin ⁡ ( 1 / x )...

mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory. The non-formalized systems...

Cantor's intersection theorem refers to two closely related theorems in general topology and real analysis, named after Georg Cantor, about intersections...

countable Cantor algebra is the Boolean algebra of all clopen subsets of the Cantor set. This is the free Boolean algebra on a countable number of generators...

the Smith normal form of a matrix. Smith was also first to discover the Cantor set. Smith was born in Dublin, Ireland, the fourth child of John Smith (1792–1828)...

the Cantor set, then every neighborhood of p contains at least one Ik, and hence at least one point of F. It follows that each point of the Cantor set lies...