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The ∞ symbol in several typefaces Infinity (symbol: ∞ ) refers to something without any limit , and is a concept relevant in a number of fields, predominantly mathematics and physics . The English word infinity derives from Latin infinitas , which can be translated as "unboundedness", itself derived from the Greek word apeiros , meaning "endless". [ 1 ] In mathematics, "infinity" is often treated as if it were a number (i.e., it counts or measures things: "an infinite number of terms") but it is not the same sort of number as the real numbers . In number systems incorporating infinitesimals , the reciprocal of an infinitesimal is an infinite number, i.e., a number greater than any real number.
By Nancy McGough ( nm @ noadsplease.ii.com ) Overview 1.1 What is the Continuum Hypothesis?
In mathematics , the continuum hypothesis (abbreviated CH ) is a hypothesis , advanced by Georg Cantor in 1878, about the possible sizes of infinite sets . It states: There is no set whose cardinality is strictly between that of the integers and that of the real numbers .
Documentary examining current ideas about very large numbers and infinity in regards to mathematics and the observable universe. By our third year, most of us will have learned to count. Once we know how, it seems as if there would be nothing to stop us counting forever.
Georg Ferdinand Ludwig Philipp Cantor ( pron.: / ˈ k æ n t ɔr / KAN -tor ; German: [ˈɡeɔʁk ˈfɛʁdinant ˈluːtvɪç ˈfɪlɪp ˈkantɔʁ] ; March 3 [ O.S. February 19] 1845 – January 6, 1918 [ 1 ] ) was a German mathematician , best known as the inventor of set theory , which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets , and proved that the real numbers are "more numerous" than the natural numbers .