What is Cantor set theory?

What is Cantor set theory?

What is Cantor set theory?

Cantor’s theorem, in set theory, the theorem that the cardinality (numerical size) of a set is strictly less than the cardinality of its power set, or collection of subsets. In symbols, a finite set S with n elements contains 2n subsets, so that the cardinality of the set S is n and its power set P(S) is 2n.

How did Cantor Discover set theory?

Cantor soon realised that he needed to define real numbers, so to speak, arithmetically and not merely as points on a line. Thus, Cantor set out to develop a satisfactory theory of real numbers.

Who is the father of set theory?

Georg Ferdinand Ludwig Philipp Cantor
Georg Cantor, in full Georg Ferdinand Ludwig Philipp Cantor, (born March 3, 1845, St. Petersburg, Russia—died January 6, 1918, Halle, Germany), German mathematician who founded set theory and introduced the mathematically meaningful concept of transfinite numbers, indefinitely large but distinct from one another.

Who is father of topology?

Mathematicians associate the emergence of topology as a distinct field of mathematics with the 1895 publication of Analysis Situs by the Frenchman Henri Poincaré, although many topological ideas had found their way into mathematics during the previous century and a half.

What is a Cantor set in maths?

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 by Henry John Stephen Smith and introduced by German mathematician Georg Cantor in 1883.

What is the Cantor set used for?

The Cantor set is the set of all numbers that can be written in base 3 using only 0’s and 2’s, not the set of all numbers that must be written this way, so we will allow 1 and 1/3 and other such numbers to be part of the set. A Cantor set tattoo adorns the arm of Lamar University math professor Robert Vallin.

Which theory was first used in mathematics?

The oldest mathematical texts from Mesopotamia and Egypt are from 2000 to 1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical concept after basic arithmetic and geometry.

Why was the set theory important?

Set theory is important mainly because it serves as a foundation for the rest of mathematics–it provides the axioms from which the rest of mathematics is built up.

When did Cantor gave birth to set theory?

Set theory, as a separate mathematical discipline, begins in the work of Georg Cantor. One might say that set theory was born in late 1873, when he made the amazing discovery that the linear continuum, that is, the real line, is not countable, meaning that its points cannot be counted using the natural numbers.