Search results
Results from the WOW.Com Content Network
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 ...
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. Because prime numbers have no non-trivial factors, this means it is less likely ...
In combinatorics, the twelvefold way is a systematic classification of 12 related enumerative problems concerning two finite sets, which include the classical problems of counting permutations, combinations, multisets, and partitions either of a set or of a number.
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, 2 is a multiplier of the (7,3,1)-difference set mentioned above. It has been mentioned that a numerical multiplier of a difference set D {\displaystyle D} in an abelian group G {\displaystyle G} fixes a translate of D {\displaystyle D} , but it can also be shown that there is a translate of D {\displaystyle D} which is fixed by all ...
In set theory in mathematics and formal logic, two sets are said to be disjoint sets if they have no element in common. Equivalently, two disjoint sets are sets whose intersection is the empty set. [1] For example, {1, 2, 3} and {4, 5, 6} are disjoint sets, while {1, 2, 3} and {3, 4, 5} are not disjoint. A collection of two or more sets is ...
In mathematics, the concepts of essential infimum and essential supremum are related to the notions of infimum and supremum, but adapted to measure theory and functional analysis, where one often deals with statements that are not valid for all elements in a set, but rather almost everywhere, that is, except on a set of measure zero.
Since the expression on the left is an integer multiple of 2, the right expression is by definition divisible by 2. That is, a 2 is even, which implies that a must also be even, as seen in the proposition above (in #Proof by contraposition). So we can write a = 2c, where c is also an integer. Substitution into the original equation yields 2b 2 ...