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:
“What makes it so plausible to assume that hypocrisy is the vice of vices is that integrity can indeed exist under the cover of all other vices except this one. Only crime and the criminal, it is true, confront us with the perplexity of radical evil; but only the hypocrite is really rotten to the core.”
—Hannah Arendt (1906–1975)
“The will is one of the chief factors in belief, not that it creates belief, but because things are true or false according to the aspect in which we look at them. The will, which prefers one aspect to another, turns away the mind from considering the qualities of all that it does not like to see; and thus the mind, moving in accord with the will, stops to consider the aspect which it likes and so judges by what it sees.”
—Blaise Pascal (1623–1662)
“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)