Cantor's infinity diagonalisation proof

Cantor's infinity diagonalisation proof

A900/0140 Rights Managed

Request low-res file

530 pixels on longest edge, unwatermarked

Request/Download high-res file

Uncompressed file size: 72.9MB

Downloadable file size: 728.4KB

Price image Pricing

Please login to use the price calculator


Credit: SCIENCE PHOTO LIBRARY

Caption: Cantor's infinity diagonalisation proof. Diagram showing how the German mathematician Georg Cantor (1845-1918) used a diagonalisation argument in 1891 to show that there are sets of numbers that are uncountable. The set of natural numbers (1, 2, 3..) is infinite, but can be shown to be countable (see A900/141). The set of real numbers (infinite decimals), however, is not countable, and is considered to be of a higher order of infinity. This is shown by constructing an array of infinite decimals to form the diagonal number (green). By subtracting one from each digit of the green number, a new number (red) has been formed that can never be found in the original infinite array. The relative sizes of such infinite sets are described by cardinal numbers.

Release details: Model release not required. Property release not required.

Keywords: cantor, cantor's, cardinal numbers, cardinality, decimal, diagonal argument, diagonalisation proof, diagram, georg cantor, group, illustration, infinite, infinity, mathematical, mathematics, maths, number, proof, rational number, real numbers, set, set theory, theory, transfinite, uncountable

Licence fees: A licence fee will be charged for any media (low or high resolution) used in your project.