Sequence FAQs:

Q: Is sequence an enumerated collection of objects in which repetitions are allowed?

A: Yes.

Q: Is sequence important in the study of sequences in metric spaces?

A: Yes, and and, in particular, in real analysis.

Q: Is sequence a means of computing homology groups by taking successive approximations?

A: Yes.

Q: Is sequence denoted by this symbol with n as subscript?

A: Yes, for example, the nth element of the Fibonacci sequence is generally denoted Fn.

Q: Is sequence related naturally to a sequence of integers whose pattern can be easily inferred?

A: Yes.

Q: Is sequence convergence?

A: Yes.

Q: Is sequence sometimes called multiplicative?

A: Yes, if anm = an am for all pairs n, m such that n and m are coprime.

Q: Is sequence said to be bounded from above?

A: Yes.

Q: Is sequence the sequence of decimal digits of π, i.e?

A: Yes, . This sequence does not have any pattern that is easily discernible by eye, unlike the preceding sequence, which is increasing.

Q: Are sequences sometimes called strings, words or lists, the different names commonly corresponding to different ways to represent them in computer memory?

A: Yes, infinite sequences are called streams.

Q: Are sequences the concept of nets?

A: Yes.

Q: Is sequence said to be monotonically increasing?

A: Yes, if each term is greater than or equal to the one before it.

Q: Is sequence a sequence whose terms are polynomials?

A: Yes.

Q: Is sequence convergent if and only if all of its subsequences are convergent?

A: Yes.

Q: Is sequence bounded and monotonic then it is convergent?

A: Yes.

Q: Is sequence 0?

A: Yes, and 1, 1, 2, 3, 5, 8, 13, 21, and 34.

Q: Is sequence a sequence whose terms are integers?

A: Yes.

Q: Are sequences also of interest in their own right and can be studied as patterns or puzzles?

A: Yes, such as in the study of prime numbers.

Q: Is sequence a sequence formed from the given sequence by deleting some of the elements without disturbing the relative positions of the remaining elements?

A: Yes.

Q: Is sequence called strictly monotonically increasing?

A: Yes.

Q: Is sequence both bounded from above and bounded from below?

A: Yes, and then the sequence is said to be bounded.

Q: Is sequence monotonically decreasing?

A: Yes, if each consecutive term is less than or equal to the previous one, and strictly monotonically decreasing, if each is strictly less than the previous.

Q: Are sequences a type of function, they are usually distinguished notationally from functions in that the input is written as a subscript rather than in parentheses, i.e?

A: Yes, an rather than f. There are terminological differences as well: the value of a sequence at the input 1 is called the "first element" of the sequence, the value at 2 is called the "second element", etc.

Q: Are sequences useful in a number of mathematical disciplines for studying functions?

A: Yes, and spaces, and other mathematical structures using the convergence properties of sequences.

Q: Is sequence called a singly infinite sequence or a one-sided infinite sequence when disambiguation is necessary?

A: Yes.

Q: Is sequence bounded from below and any such m is called a lower bound?

A: Yes.

Q: Is sequence a sequence whose terms become arbitrarily close together as n gets very large?

A: Yes.

Q: Are sequences called complete metric spaces and are particularly nice for analysis?

A: Yes.

Q: Are sequences a generalization of exact sequences?

A: Yes, and since their introduction by Jean Leray , they have become an important research tool, particularly in homotopy theory.

Q: Is sequence either increasing or decreasing it is called a monotone sequence?

A: Yes.

Q: Are sequences the basis for series?

A: Yes, and which are important in differential equations and analysis.

Q: Is sequence its rank or index?

A: Yes, it is the integer from which the element is the image.

Q: Are sequences sometimes called the Cantor space?

A: Yes.

Q: Is sequence to list the elements?

A: Yes.

Q: Is sequence a generalization of a sequence?

A: Yes.

Q: Is sequence an ordinary sequence?

A: Yes.

Q: Are sequences numerical ones?

A: Yes, that is, sequences of real or complex numbers.

Q: Is sequence discussed after the examples?

A: Yes.

Q: Is sequence defined as the number of terms in the sequence?

A: Yes.