Infinity - Wikipedia, the free encyclopedia
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Infinity (symbolically represented by ∞ ) refers to several distinct concepts – usually linked to the idea of "without end" – which arise in philosophy, mathematics, and theology. The word comes fr...
en.wikipedia.org/wiki/Infinity
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Hyperreal number - Wikipedia, the free encyclopedia
The system of hyperreal numbers represents a rigorous method of treating the infinite and infinitesimal numbers that had been widely used by mathematicians, scientists, and engineers ever since the ...
en.wikipedia.org/wiki/Hyperreal_number
Is there an infinite number of primes? ... Are Prime Numbers Infinite? How do we know the number of primes is infinite? ... Primes and Perfect Numbers Are there infinite numbers of prime and perfect numbers?
mathforum.org/library/drmath/sets/select/dm_infinite_pr... mathforum.org/library/drmath/sets/select/dm_infinite_primes.html
An example of something that is uncountably infinite would be all the real numbers (including numbers like 2.34.. and the square root of 2, as well as all the integers and rational numbers). In fact, there are more real numbers between 0 and 1 than there are natural numbers (1,2,3,4,...) in the whole number line!
mathforum.org/dr.math/faq/faq.large.numbers.html mathforum.org/dr.math/faq/faq.large.numbers.html
for example, {A, B, C} = {B, A, C}. In this brief exposition, I introduce the mathematics of infinite cardinal numbers and ignore the infinite ordinals.
www.earlham.edu/~peters/writing/infapp.htm
Any infinite set of real numbers is either countably infinite or has the same cardinality as the entire set of real numbers. ... Without the Axiom of Choice, there is no guarantee that infinite cardinal numbers are comparable. Cardinal numbers can form a partially ordered set and aleph1 and c might be on two...
www.ii.com/math/ch/
These concepts that describe the sizes of infinite sets are called infinite cardinal numbers. ... There are also different cardinal numbers that describe the sizes of sets (such as the set of real numbers) that are not the same size as the set of integers. There are in fact infinitely many different infinite cardinal numbers!
www.math.toronto.edu/mathnet/plain/answers/infcardinal.... www.math.toronto.edu/mathnet/plain/answers/infcardinal.html
Set Theory and Infinite Numbers ... The first consistent theory of infinite numbers was created just over a century ago by the German mathematician Georg Cantor (1845-1918). In this presentation, I shall introduce you to the most basic concepts of Cantor's theory.
www.math.toronto.edu/mathnet/simmer/topic.feb98.html
So far so good. Now what about infinite sets? Are there the same number of even whole numbers, as there are of all whole numbers -- or should there be only half as many even whole numbers?
fclass.vaniercollege.qc.ca/web/mathematics/real/infinit... fclass.vaniercollege.qc.ca/web/mathematics/real/infinity.htm
Stanford mathematician Keith Devlin will moderate a discussion on the subject of infinite numbers at the annual meeting of the American Mathematical Society. He talks about the concept of infinity with NPR's Scott Simon. ... Also heard on NPR stations: ... This American Life PRI...
www.npr.org/templates/story/story.php?storyId=4234905
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