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One of the earliest examples of this is The Sand Reckoner, in which Archimedes gave a system for naming large numbers. To do this, he called the numbers up to a myriad myriad (10 8) "first numbers" and called 10 8 itself the "unit of the second numbers".
Large numbers, far beyond those encountered in everyday life—such as simple counting or financial transactions—play a crucial role in various domains.These expansive quantities appear prominently in mathematics, cosmology, cryptography, and statistical mechanics.
Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.
Kasner used it to illustrate the difference between an unimaginably large number and infinity, and in this role it is sometimes used in teaching mathematics. To put in perspective the size of a googol, the mass of an electron, just under 10 −30 kg, can be compared to the mass of the visible universe, estimated at between 10 50 and 10 60 kg. [ 5 ]
Far larger finite numbers than any of these occur in modern mathematics. For instance, Graham's number is too large to reasonably express using exponentiation or even tetration. For more about modern usage for large numbers, see Large numbers. To handle these numbers, new notations are created and used. There is a large community of ...
They are called the strong law of large numbers and the weak law of large numbers. [ 16 ] [ 1 ] Stated for the case where X 1 , X 2 , ... is an infinite sequence of independent and identically distributed (i.i.d.) Lebesgue integrable random variables with expected value E( X 1 ) = E( X 2 ) = ... = μ , both versions of the law state that the ...
Big numbers may refer to: Large numbers, numbers that are significantly larger than those ordinarily used in everyday life; Arbitrary-precision arithmetic, also called bignum arithmetic; Big Numbers, an unfinished comics series by Alan Moore and Bill Sienkiewicz
Empty numbers are sometimes made up, with obvious meaning: "squillions" is obviously an empty, but very large, number; a "squintillionth" would be a very small number. Some empty numbers may be modified by actual numbers, such as "four zillion", and are used for jest, exaggeration, or to relate abstractly to actual numbers.