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In mathematics, the factorial of a non-negative integer , denoted by , is the product of all positive integers less than or equal to . The factorial of also equals the product of with the next smaller factorial: For example, The value of 0! is 1, according to the convention for an empty product. [1]
[6] The decay time for a supermassive black hole of roughly 1 galaxy-mass ( 10 11 solar masses ) due to Hawking radiation is on the order of 10 100 years . [ 7 ] Therefore, the heat death of an expanding universe is lower-bounded to occur at least one googol years in the future.
The factorial number system is sometimes defined with the 0! place omitted because it is always zero (sequence A007623 in the OEIS). In this article, a factorial number representation will be flagged by a subscript "!". In addition, some examples will have digits delimited by a colon. For example, 3:4:1:0:1:0! stands for
Roughly speaking, the simplest version of Stirling's formula can be quickly obtained by approximating the sum with an integral: The full formula, together with precise estimates of its error, can be derived as follows. Instead of approximating , one considers its natural logarithm, as this is a slowly varying function:
6.5 × 10 −4966 is ... 69! (roughly 1.7112245 × 10 98), is the largest factorial value that can be represented on a calculator with two digits for powers of ten ...
Factorion. In number theory, a factorion in a given number base is a natural number that equals the sum of the factorials of its digits. [1][2][3] The name factorion was coined by the author Clifford A. Pickover. [4]
The falling factorial can be extended to real values of using the gamma function provided and + are real numbers that are not negative integers: = (+) (+) , and so can the rising factorial: = (+) . Calculus
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 ...