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:
“The idea that information can be stored in a changing world without an overwhelming depreciation of its value is false. It is scarcely less false than the more plausible claim that after a war we may take our existing weapons, fill their barrels with cylinder oil, and coat their outsides with sprayed rubber film, and let them statically await the next emergency.”
—Norbert Wiener (1894–1964)
“What makes all doctrines plain and clear?
About two hundred pounds a year.
And that which was proved true before
Prove false again? Two hundred more.”
—Samuel Butler (1612–1680)
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (1533–1592)