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In mathematics, a tuple is a finite sequence or ordered list of numbers or, more generally, mathematical objects, ... In computer science, tuples come in many forms.
Permutations are used in almost every branch of mathematics and in many other fields of science. ... Donald (2005), Generating All Tuples and Permutations, The Art of ...
Ordered pairs are also called 2-tuples, or sequences (sometimes, lists in a computer science context) of length 2. Ordered pairs of scalars are sometimes called 2-dimensional vectors . (Technically, this is an abuse of terminology since an ordered pair need not be an element of a vector space .)
An example of a deterministic finite automaton that accepts only binary numbers that are multiples of 3. The state S 0 is both the start state and an accept state. For example, the string "1001" leads to the state sequence S 0, S 1, S 2, S 1, S 0, and is hence accepted.
They occur in a number of branches of mathematics and physics, ... For example, the partition 2 + 2 + 1 might instead be written as the tuple (2, 2, 1) ...
An NFA is represented formally by a 5-tuple, (,,,,), consisting of a finite set of states Q {\displaystyle Q} , a finite set of input symbols called the alphabet Σ {\displaystyle \Sigma } ,
Cartesian coordinates identify points of the Euclidean plane with pairs of real numbers. In mathematics, the real coordinate space or real coordinate n-space, of dimension n, denoted R n or , is the set of all ordered n-tuples of real numbers, that is the set of all sequences of n real numbers, also known as coordinate vectors.
The equality ((+)) = (()) can also be understood as an equivalence of different counting problems: the number of k-tuples of non-negative integers whose sum is n equals the number of (n + 1)-tuples of non-negative integers whose sum is k − 1, which follows by interchanging the roles of bars and stars in the diagrams representing configurations.