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It can be thought of as a number that is bigger than any other conceivable or inconceivable quantity, either finite or transfinite. Cantor linked the absolute infinite with God , [ 1 ] [ 2 ] : 175 [ 3 ] : 556 and believed that it had various mathematical properties, including the reflection principle : every property of the absolute infinite is ...
Notably, ℵ ω is the first uncountable cardinal number that can be demonstrated within Zermelo–Fraenkel set theory not to be equal to the cardinality of the set of all real numbers 2 ℵ 0: For any natural number n ≥ 1, we can consistently assume that 2 ℵ 0 = ℵ n, and moreover it is possible to assume that 2 ℵ 0 is as least as large ...
Centillion [12] appears to be the highest name ending in -"illion" that is included in these dictionaries. Trigintillion , often cited as a word in discussions of names of large numbers, is not included in any of them, nor are any of the names that can easily be created by extending the naming pattern ( unvigintillion , duovigintillion , duo ...
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
Euler ascertained that 2 31 − 1 = 2147483647 is a prime number; and this is the greatest at present known to be such, and, consequently, the last of the above perfect numbers [i.e., 2 30 (2 31 − 1)], which depends upon this, is the greatest perfect number known at present, and probably the greatest that ever will be discovered; for as they ...
The ultimate in large numbers was, until recently, the concept of infinity, a number defined by being greater than any finite number, and used in the mathematical theory of limits. However, since the 19th century, mathematicians have studied transfinite numbers , numbers which are not only greater than any finite number, but also, from the ...
And after this first term, still another 63 terms remain in the rapidly growing g sequence before Graham's number G = g 64 is reached. To illustrate just how fast this sequence grows, while g 1 is equal to 3 ↑ ↑ ↑ ↑ 3 {\displaystyle 3\uparrow \uparrow \uparrow \uparrow 3} with only four up arrows, the number of up arrows in g 2 is this ...
Many possible bounded, flat possibilities also exist for three-dimensional space. [55] The concept of infinity also extends to the multiverse hypothesis, which, when explained by astrophysicists such as Michio Kaku, posits that there are an infinite number and variety of universes. [56]