Sequences
... which the difference between any two consecutive terms is a constant. In other words, it is a sequence of numbers in which a positive or negative constant is added to each term to produce the next term. This positive or negative constant is called the common difference. The common difference is typi ...
... which the difference between any two consecutive terms is a constant. In other words, it is a sequence of numbers in which a positive or negative constant is added to each term to produce the next term. This positive or negative constant is called the common difference. The common difference is typi ...
Pigeonhole Solutions
... remainders upon dividing by n: their “residues.” Equivalently, write all numbers base n and just look at the one’s digit. This algebraic structure—a commutative ring—is called Z/nZ. All the usual rules of arithmetic still work: the identity properties of zero and one, the commutative and associative ...
... remainders upon dividing by n: their “residues.” Equivalently, write all numbers base n and just look at the one’s digit. This algebraic structure—a commutative ring—is called Z/nZ. All the usual rules of arithmetic still work: the identity properties of zero and one, the commutative and associative ...
Application of Linear Sequences to Cryptography
... Because the idea of cryptography is to transmit information under the radar, the sequence to be used should be well disguised. The Fibonacci sequence is such a widely known mathematical sequence that Sherlock Holmes was able to easily decipher Moriarty’s code and foil his plans. Being able to utiliz ...
... Because the idea of cryptography is to transmit information under the radar, the sequence to be used should be well disguised. The Fibonacci sequence is such a widely known mathematical sequence that Sherlock Holmes was able to easily decipher Moriarty’s code and foil his plans. Being able to utiliz ...
Sequences and Limit of Sequences
... Like a function, a sequence can be plotted. However, since the domain is a subset of Z, the plot will consist of dots instead of a continuous curve. Since a sequence is de…ned as a function. everything we de…ned for functions (bounds, supremum, in…mum, ...) also applies to sequences. We restate thos ...
... Like a function, a sequence can be plotted. However, since the domain is a subset of Z, the plot will consist of dots instead of a continuous curve. Since a sequence is de…ned as a function. everything we de…ned for functions (bounds, supremum, in…mum, ...) also applies to sequences. We restate thos ...
Sequence
In mathematics, a sequence is an ordered collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Formally, a sequence can be defined as a function whose domain is a countable totally ordered set, such as the natural numbers.For example, (M, A, R, Y) is a sequence of letters with the letter 'M' first and 'Y' last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be finite, as in these examples, or infinite, such as the sequence of all even positive integers (2, 4, 6,...). In computing and computer science, finite sequences are sometimes called strings, words or lists, the different names commonly corresponding to different ways to represent them into computer memory; infinite sequences are also called streams. The empty sequence ( ) is included in most notions of sequence, but may be excluded depending on the context.