Strong Law of Small Numbers

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In mathematics, the "Strong Law of Small Numbers" is the humorous law that proclaims, in the words of Richard K. Guy (1988):[1]

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.[2] Guy's paper gives 35 examples in support of this thesis. This can lead inexperienced mathematicians to conclude that these concepts are related, when in fact they are not.[3]

Guy also formulated the Second Strong Law of Small Numbers:

When two numbers look equal, it ain't necessarily so![4]

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.[4]

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  1. ^ 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.
  2. ^ Gardner, M. "Mathematical Games: Patterns in Primes are a Clue to the Strong Law of Small Numbers." Sci. Amer. 243, 18-28, Dec. 1980.
  3. ^ "". Retrieved 2019-05-07.
  4. ^ a b Guy, Richard K. (1990). "The Second Strong Law of Small Numbers". Mathematics Magazine. 63 (1): 3–20. doi:10.2307/2691503. JSTOR 2691503.

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