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Revision as of 08:25, 2 March 2021 by Salix alba (talk | contribs) (rv possible sock. Add some examples taken from Guy and link to relevant wikipedia articles)(diff) ← Previous revision | Latest revision (diff) | Newer revision → (diff) Humorous mathematical law For other uses, see Law of small numbers (disambiguation).
In mathematics, the "Strong Law of Small Numbers" is the humorous law that proclaims, in the words of Richard K. Guy (1988):
There aren't enough small numbers to meet the many demands made of them.
In other words, any given small number appears in far more contexts than may seem reasonable, leading to many apparently surprising coincidences in mathematics, simply because small numbers appear so often and yet are so few. Earlier (1980) this "law" was reported by Martin Gardner. Guy's paper gives numerous examples in support of this thesis.
Guy also formulated the Second Strong Law of Small Numbers:
When two numbers look equal, it ain't necessarily so!
Guy explains the latter law by the way of examples: he cites numerous sequences for which observing a subset of the first few members may lead to a wrong guess about the generating formula or law for the sequence. Many of the examples are the observations of other mathematicians.
Some examples Guy gives include the Moser's circle problem, Mersenne prime where is prime when is one of the first few primes but fails for , and the Prime number race where primes congruent to 3 modulo 4 appear to be more numerous that those congruent to 1, this first fails for primes less than 26861.
is prime when 
is one of the first few primes but fails for 
, and the See also
- Insensitivity to sample size
- Law of large numbers (unrelated, but the origin of the name)
- Mathematical coincidence
- Pigeonhole principle
- Representativeness heuristic
Notes
- Guy, Richard K. (1988). "The Strong Law of Small Numbers" (PDF). American Mathematical Monthly. 95 (8): 697–712. doi:10.2307/2322249. ISSN 0002-9890. JSTOR 2322249. Retrieved 2009-08-30.
- Gardner, M. "Mathematical Games: Patterns in Primes are a Clue to the Strong Law of Small Numbers." Sci. Amer. 243, 18-28, Dec. 1980.
- ^ Guy, Richard K. (1990). "The Second Strong Law of Small Numbers". Mathematics Magazine. 63 (1): 3–20. doi:10.2307/2691503. JSTOR 2691503.
External links
- Caldwell, Chris. "Law of small numbers". The Prime Glossary.
- Weisstein, Eric W. "Strong Law of Small Numbers". MathWorld.
- Carnahan, Scott (2007-10-27). "Small finite sets". Secret Blogging Seminar, notes on a talk by Jean-Pierre Serre on properties of small finite sets.
{{cite web}}: CS1 maint: postscript (link) - Amos Tversky; Daniel Kahneman (August 1971). "Belief in the law of small numbers". Psychological Bulletin. 76 (2): 105–110. CiteSeerX 10.1.1.592.3838. doi:10.1037/h0031322.
people have erroneous intuitions about the laws of chance. In particular, they regard a sample randomly drawn from a population as highly representative, I.e., similar to the population in all essential characteristics.
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