What is a strictly increasing sequence?

What is a strictly increasing sequence?

In words, a sequence is strictly increasing if each term in the sequence is larger than the preceding term and strictly decreasing if each term of the sequence is smaller than the preceding term. One way to determine if a sequence is strictly increasing is to show the n. th. term of the sequence.

How do you tell if a series is increasing or decreasing?

If an, then the sequence is increasing or strictly increasing . If an≤an+1 a n ≤ a n + 1 for all n, then the sequence is non-decreasing . If an>an+1 a n > a n + 1 for all n, then the sequence is decreasing or strictly decreasing .

What is a well defined sequence?

In general “well-defined” means that some object was given a description up to some arbitrary choices, but that the arbitrary choices have no material effect. endgroup.

What is an increasing sequence of sets?

Let S=P(S) be the power set of S. Let ⟨Sk⟩k∈N be a nested sequence of subsets of S such that: ∀k∈N:Sk⊆Sk+1. Then ⟨Sk⟩k∈N is an increasing sequence of sets (in S).

Can a sequence increase and decrease?

Note that in order for a sequence to be increasing or decreasing it must be increasing/decreasing for every n . In other words, a sequence that increases for three terms and then decreases for the rest of the terms is NOT a decreasing sequence!

What is almost increasing sequence?

A sequence of numbers is said to be in a strictly increasing sequence if every succeeding element in the sequence is greater than its preceding element. The function should check whether we can form a strictly increasing sequence of the numbers by removing no more than one element from the array.

How do you know if a sequence is decreasing?

Section 4-2 : More on Sequences

1. We call the sequence increasing if an
2. We call the sequence decreasing if an>an+1 a n > a n + 1 for every n .
3. If {an} is an increasing sequence or {an} is a decreasing sequence we call it monotonic.

How do you prove a relation is well-defined?

A function is well defined if it gives the same result when the representation of the input is changed without changing the value of the input. For instance, if f takes real numbers as input, and if f(0.5) does not equal f(1/2) then f is not well defined (and thus not a function).

How do you prove a mapping is well-defined?

Let S/R be the quotient set determined by R. Let ϕ:S/R→T be a mapping such that: ϕ([[x]]R)=f(x) Then ϕ:S/R→T is well-defined if and only if: ∀(x,y)∈R:f(x)=f(y)