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This template's initial visibility currently defaults to autocollapse, meaning that if there is another collapsible item on the page (a navbox, sidebar, or table with the collapsible attribute), it is hidden apart from its title bar; if not, it is fully visible. To change this template's initial visibility, the |state= parameter may be used:
Numbers uses a free-form "canvas" approach that demotes tables to one of many different media types placed on a page. Other media, like charts , graphics , and text, are treated as peers. In comparison, traditional spreadsheets like Microsoft Excel use the table as the primary container, with other media placed within the table.
This operation is not free since the integer 0 can be written pair(0,0), or pair(1,1), or pair(2,2), etc.. This technique of construction is used by the proof assistant Isabelle ; however, many other tools use alternative construction techniques, notable those based upon free constructors, which are simpler and can be implemented more ...
The sum a + b can be interpreted as a binary operation that combines a and b, in an algebraic sense, or it can be interpreted as the addition of b more units to a. Under the latter interpretation, the parts of a sum a + b play asymmetric roles, and the operation a + b is viewed as applying the unary operation +b to a. [20]
For example, the set of odd numbers is a sum-free subset of the integers, and the set {N + 1, ..., 2N } forms a large sum-free subset of the set {1, ..., 2N }. Fermat's Last Theorem is the statement that, for a given integer n > 2, the set of all nonzero n th powers of the integers is a sum-free set.
In additive combinatorics, the sumset (also called the Minkowski sum) of two subsets and of an abelian group (written additively) is defined to be the set of all sums of an element from with an element from .