Search results
Results from the WOW.Com Content Network
where is the set of square numbers. A subject that has received a fair amount of study is that of sets with small doubling , where the size of the set A + A {\displaystyle A+A} is small (compared to the size of A {\displaystyle A} ); see for example Freiman's theorem .
The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".
The Minkowski sum of two sets and of real numbers is the set + := {+:,} consisting of all possible arithmetic sums of pairs of numbers, one from each set. The infimum and supremum of the Minkowski sum satisfy, if A ≠ ∅ ≠ B {\displaystyle A\neq \varnothing \neq B} inf ( A + B ) = ( inf A ) + ( inf B ) {\displaystyle \inf(A+B)=(\inf A ...
To prove the inclusion–exclusion principle for the cardinality of sets, sum the equation over all x in the union of A 1, ..., A n. To derive the version used in probability, take the expectation in . In general, integrate the equation with respect to μ. Always use linearity in these derivations.
In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
The natural sum and natural product operations on ordinals were defined in 1906 by Gerhard Hessenberg, and are sometimes called the Hessenberg sum (or product) (Sierpiński 1958). The natural sum of α and β is often denoted by α ⊕ β or α # β, and the natural product by α ⊗ β or α ⨳ β. The natural sum and product are defined as ...
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
The red figure is the Minkowski sum of blue and green figures. In geometry, the Minkowski sum of two sets of position vectors A and B in Euclidean space is formed by adding each vector in A to each vector in B: