For-example-the-Mertens-conjecture-is-a-statemen

For example, the Mertens conjecture is a statement about natural numbers that is now known to be false, but no explicit counterexample ( i. e., a natural number n for which the Mertens function M ( n ) equals or exceeds the square root of n ) is known: all numbers less than 10 14 have the Mertens property, and the smallest number which does not have this property is only known to be less than the exponential of 1. 59 × 10 40 , which is approximately 10 to the power 4. 3 × 10 39 .

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For and example

For the family is the simplest example of just such a unit, composed of people, which gives us both some immunity from, and a way of dealing with, other people.

For example, suppose a man wearing a $200 watch, driving a 1959 Rolls Royce, stops to ask a man on the sidewalk, `` What time is it ''??

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For example, No. 56 printed the patent giving the Electoral Prince the title of Duke of Cambridge.

For example, he captured some persons from York County, who with teams were taking to Philadelphia the furniture of a man who had just been released from prison through the efforts of his wife, and who apparently was helpless to prevent the theft of his household goods.

For example, even the most successful executive lives in a two-room apartment while ordinary people rent space in the stairwells of office buildings in which to sleep at night ; ;

For example, in the third chapter of Matthew, verses 13-16, describing the baptism of Jesus, the 1611 version reads:

For example: 1.

For example, it probably will be necessary for the Corps to have authority to pay medical expenses of volunteers.

For example, the importance of the Regulus 2, a very promising aerodynamic ship-to-surface missile designed to be launched by surfaced submarines, was greatly diminished by the successful acceleration of the much more advanced Polaris ballistic missile launched by submerged submarines.

For example, the interest of past members of the Foundation's Advisory Board remains such that they place their knowledge and judgments at our disposal much as they had done when they were, formally, members of that Board.

For example, out of the social evils of the English industrial revolution came the novels of Charles Dickens ; ;

For example, a 12-to-one engine would power a supersonic VTOL fighter.

For example: Af.

For example, for the problem Af, 10 from 25 equals 15, then 6 from 15 equals 9.

For example: Af.

For example, let's consider a standard 283 cubic inch Chevy Aj.

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For and conjecture

For example: the similarity of southern continent geological formations had led Roberto Mantovani to conjecture in 1889 and 1909 that all the continents had once been joined into a supercontinent ( now known as Pangaea ); Wegener noted the similarity of Mantovani's and his own maps of the former positions of the southern continents.

For instance, the Collatz conjecture, which concerns whether or not certain sequences of integers terminate, has been tested for all integers up to 1. 2 × 10 < sup > 12 </ sup > ( over a trillion ).

For example, the Riemann hypothesis is a conjecture from number theory that ( amongst other things ) makes predictions about the distribution of prime numbers.

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:: Kakeya maximal function conjecture: For all, there exists a constant such that for any function f and all,

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As Grünbaum writes, simplicial arrangements “ appear as examples or counterexamples in many contexts of combinatorial geometry and its applications .” For instance, use simplicial arrangements to construct counterexamples to a conjecture on the relation between the degree of a set of differential equations and the number of invariant lines the equations may have.

For example the difference between a counterexample to a lemma ( a so-called ' local counterexample ') and a counterexample to the specific conjecture under attack ( a ' global counterexample ' to the Euler characteristic, in this case ) are discussed.

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For elliptic curves over the rational numbers, the Hasse – Weil conjecture follows from the modularity theorem.

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