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...

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...

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...

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

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

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...

when considered as subsets of the real numbers. The Cantor set is an example of an uncountable null set. It is uncountable because it contains all real numbers...

Cantor's diagonal argument (among various similar names) is a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence...

{\displaystyle \beth _{1}} (beth-one). The Cantor set is an uncountable subset of ⁠ R {\displaystyle \mathbb {R} } ⁠. The Cantor set is a fractal and has Hausdorff...

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...

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...

cardinality of a finite set is the number of its elements, and is therefore a measure of size of the set. Since the discovery by Georg Cantor, in the late 19th...

development of set theory was a naive set theory. It was created at the end of the 19th century by Georg Cantor as part of his study of infinite sets and developed...

\mathbb {R} ,} since the closure has empty interior. The Cantor set is an uncountable nowhere dense set in R . {\displaystyle \mathbb {R} .} R {\displaystyle...

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...

Schröder. It is also known as the Cantor–Bernstein theorem or Cantor–Schröder–Bernstein theorem, after Georg Cantor, who first published it (albeit without...

}{\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...

Riemann-integrable. The function is defined by making use of the Smith–Volterra–Cantor set and an infinite number or "copies" of sections of the function defined...

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)...

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...

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...

{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...

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...

}{\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...

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...

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 = [...

knowledge, including Cantor's theory of infinite sets. One potential application of infinite set theory is in genetics and biology. The set of all integers...

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...

"draw forward" and B mean "move forward". This produces the famous Cantor's fractal set on a real straight line R. A variant of the Koch curve which uses...

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...