Plausible But False Examples
Some plausible relations hold to a high degree of accuracy, but are still not true. One example is:
The two sides of this expression only differ after the 42nd decimal place.
Another example is that the maximum height (maximum absolute value of coefficients) of all the factors of xn − 1 appears to be the same as height of nth cyclotomic polynomial. This was shown by computer to be true for n < 10000 and was expected to be true for all n. However, a larger computer search showed that this equality fails to hold for n = 14235, when the height of the nth cyclotomic polynomial is 2, but maximum height of the factors is 3.
Read more about this topic: Experimental Mathematics
Famous quotes containing the words plausible, false and/or examples:
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—Norbert Wiener (1894–1964)
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—Mary Wollstonecraft (1759–1797)
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)