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An example of mathematics' explanatory indispensability presented by Baker is the periodic cicada, a type of insect that usually has life cycles of 13 or 17 years. It is hypothesized that this is an evolutionary advantage because 13 and 17 are prime numbers .
The Quine–Putnam indispensability argument supports the conclusion that mathematical objects exist with the idea that mathematics is indispensable to the best scientific theories. [5] It relies on the view, called confirmational holism , that scientific theories are confirmed as wholes, and that the confirmations of science extend to the ...
Example 2 For the whole numbers greater than two, being odd is necessary to being prime, since two is the only whole number that is both even and prime. Example 3 Consider thunder, the sound caused by lightning. One says that thunder is necessary for lightning, since lightning never occurs without thunder. Whenever there is lightning, there is ...
For example, the Commonwealth of Virginia does not recognize the doctrine of indispensable parties. Although a defendant may argue that the plaintiff has improperly failed to join a party that would conventionally be deemed indispensable and may seek to have the court attempt to join the missing party, if it is not feasible to join the missing ...
One of the basic principles of algebra is that one can multiply both sides of an equation by the same expression without changing the equation's solutions. However, strictly speaking, this is not true, in that multiplication by certain expressions may introduce new solutions that were not present before. For example, consider the following ...
For example, if one takes the function () that is equal to zero everywhere except at = where () =, then the supremum of the function equals one. However, its essential supremum is zero since (under the Lebesgue measure ) one can ignore what the function does at the single point where f {\displaystyle f} is peculiar.
This inverse has a special structure, making the principle an extremely valuable technique in combinatorics and related areas of mathematics. As Gian-Carlo Rota put it: [ 6 ] "One of the most useful principles of enumeration in discrete probability and combinatorial theory is the celebrated principle of inclusion–exclusion.
In mathematics, an argument of a function is a value provided to obtain the function's result. It is also called an independent variable. [1] For example, the binary function (,) = + has two arguments, and , in an ordered pair (,).