Search results
Results from the WOW.Com Content Network
In mathematics, Kruskal's tree theorem states that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under homeomorphic embedding. History [ edit ] The theorem was conjectured by Andrew Vázsonyi and proved by Joseph Kruskal ( 1960 ); a short proof was given by Crispin Nash-Williams ( 1963 ).
In probability theory, the law of large numbers ( LLN) is a mathematical theorem that states that the average of the results obtained from a large number of independent random samples converges to the true value, if it exists. [1] More formally, the LLN states that given a sample of independent and identically distributed values, the sample ...
Graham's number. Graham's number is an immense number that arose as an upper bound on the answer of a problem in the mathematical field of Ramsey theory. It is much larger than many other large numbers such as Skewes's number and Moser's number, both of which are in turn much larger than a googolplex. As with these, it is so large that the ...
The definition of Rayo's number is a variation on the definition: [5] The smallest number bigger than any finite number named by an expression in the language of first-order set theory with a googol symbols or less. Specifically, an initial version of the definition, which was later clarified, read "The smallest number bigger than any number ...
Large numbers. Large numbers are numbers significantly larger than those typically used in everyday life (for instance in simple counting or in monetary transactions), appearing frequently in fields such as mathematics, cosmology, cryptography, and statistical mechanics.
a number n in a triangle means n n. a number n in a square is equivalent to "the number n inside n triangles, which are all nested." a number n in a pentagon is equivalent with "the number n inside n squares, which are all nested." etc.: n written in an (m + 1)-sided polygon is equivalent with "the number n inside n nested m-sided polygons".
Coprime integers. In number theory, two integers a and b are coprime, relatively prime or mutually prime if the only positive integer that is a divisor of both of them is 1. [1] Consequently, any prime number that divides a does not divide b, and vice versa. This is equivalent to their greatest common divisor (GCD) being 1. [2]
Sagan gave an example that if the entire volume of the observable universe is filled with fine dust particles roughly 1.5 micrometers in size (0.0015 millimeters), then the number of different combinations in which the particles could be arranged and numbered would be about one googolplex.