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In this usage, infinity is a mathematical concept, and infinite mathematical objects can be studied, manipulated, and used just like any other mathematical object. The mathematical concept of infinity refines and extends the old philosophical concept, in particular by introducing infinitely many different sizes of infinite sets.
It has been noted that, in an earlier work, Wallis came to the conclusion that the ratio of a positive number to a negative one is greater than infinity. The argument involves the quotient 1 x {\displaystyle {\tfrac {1}{x}}} and considering what happens as x {\displaystyle x} approaches and then crosses the point x = 0 {\displaystyle x=0} from ...
The infinity symbol (∞) is a mathematical symbol representing the concept of infinity. This symbol is also called a lemniscate , [ 1 ] after the lemniscate curves of a similar shape studied in algebraic geometry , [ 2 ] or "lazy eight", in the terminology of livestock branding .
In philosophy and theology, infinity is explored in articles under headings such as the Absolute, God, and Zeno's paradoxes. In Greek philosophy , for example in Anaximander , 'the Boundless' is the origin of all that is.
Srinivasa Ramanujan Aiyangar [a] (22 December 1887 – 26 April 1920) was an Indian mathematician.Often regarded as one of the greatest mathematicians of all time, though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then ...
God Created the Integers: The Mathematical Breakthroughs That Changed History is a 2005 anthology, edited by Stephen Hawking, of "excerpts from thirty-one of the most important works in the history of mathematics." [1] Each chapter of the work focuses on a different mathematician and begins with a biographical overview. Within each chapter ...
Accordingly I distinguish an eternal uncreated infinity or absolutum, which is due to God and his attributes, and a created infinity or transfinitum, which has to be used wherever in the created nature an actual infinity has to be noticed, for example, with respect to, according to my firm conviction, the actually infinite number of created ...
Georg Ferdinand Ludwig Philipp Cantor (/ ˈ k æ n t ɔːr / KAN-tor; German: [ˈɡeːɔʁk ˈfɛʁdinant ˈluːtvɪç ˈfiːlɪp ˈkantoːɐ̯]; 3 March [O.S. 19 February] 1845 – 6 January 1918 [1]) was a mathematician who played a pivotal role in the creation of set theory, which has become a fundamental theory in mathematics.