[‚män·ə‚tōn ¦nän·di′krēs·iŋ ‚fəŋk·shən] (mathematics) A function which never decreases, that is, if x ≤ y then ƒ(x) ≤ ƒ(y). Also known as monotone increasing function; monotonically nondecreasing function.

What is Nondecreasing?

Non-decreasing means that no element is less than the element before it, or in other words: that every element is greater than or equal to the one before it.

What is a monotonic transformation?

A monotonic transformation is a way of transforming one set of numbers into another set of numbers in a way that the order of the numbers is preserved. If the original utility function is U(x,y), we represent. a monotonic transformation by [ ]

What is monotone property?

A property is called monotone if it is closed under taking subgraphs and hereditary if it is closed under taking only induced subgraphs. Clearly, each monotone property is hereditary, but the converse is not true.

What is monotone sequence?

Monotone Sequences. Definition : We say that a sequence (xn) is increasing if xn ≤ xn+1 for all n and strictly increasing if xn < xn+1 for all n. Similarly, we define decreasing and strictly decreasing sequences. Sequences which are either increasing or decreasing are called monotone.

Monotonic Sequences and Bounded Sequences - Calculus 2

17 related questions found

What is monotone voice?

a vocal utterance or series of speech sounds in one unvaried tone. a single tone without harmony or variation in pitch. ... a person who is unable to discriminate between or to reproduce differences in musical pitch, especially in singing.

What is monotone physics?

The sound with unvaried pitch is called monotone sound.

What is monotone math?

A monotonic function is a function which is either entirely nonincreasing or nondecreasing. A function is monotonic if its first derivative (which need not be continuous) does not change sign.

What is monotonic in calculus?

In calculus, a function. defined on a subset of the real numbers with real values is called monotonic if and only if it is either entirely non-increasing, or entirely non-decreasing. That is, as per Fig. 1, a function that increases monotonically does not exclusively have to increase, it simply must not decrease.

How do you prove a function is monotone?

Test for monotonic functions states: Suppose a function is continuous on [a, b] and it is differentiable on (a, b). If the derivative is larger than zero for all x in (a, b), then the function is increasing on [a, b]. If the derivative is less than zero for all x in (a, b), then the function is decreasing on [a, b].

Is the inverse of a monotone function monotone?

So a monotonic function has an inverse iff it is strictly monotonic.

What is nondecreasing sequence?

Non-decreasing sequences are a generalization of binary covering arrays, which has made research on non-decreasing sequences important in both math and computer science. The goal of this research is to find properties of these non- decreasing sequences as the variables d, s, and t change.

How do you know if a function is Nondecreasing?

The usual way of proving that a function is non-decreasing is to analyze the sign of its first derivative: roughly, given a function f, it will be non-decreasing if f′(x)≥0. Since your function is continuous and has no singularity, you just need to compute F′ and observe that it can never be negative.

What are increasing functions?

A function is "increasing" when the y-value increases as the x-value increases, like this: It is easy to see that y=f(x) tends to go up as it goes along.

What causes monotone?

This visual or verbal absent can be caused by conditions that include schizophrenia, autism, depression, and traumatic brain injury. Emotions to stimuli that are not expressed by people with flat affect include facial, voice and body language changes.

What is called monotone draw a waveform of a monotone?

Answer: As the function describing the profile is (strictly) monotonic, the resulting travelling wave is called a monotone wave. For a general system of PDEs allowing travelling wave solutions however, all kinds of wave profiles are possible.

Is monotone a bad thing?

The Speech Problem: Monotone Voice

Speaking in a monotone voice is a real communication killer. When the variety of your voice's pitch doesn't vary, it's impossible for your listener to maintain any interest in what you're saying.

What is monotone example?

Monotone is a continuous sound, especially of someone speaking, that doesn't change in pitch or inflection. An example of a monotone is when someone has a dull-flat voice, like Ben Stein. ... If you paint every room in your house the same dull flat beige, this is an example of a time when your house is monotone.

What is monotone voice in presentation?

So what does it mean to have a monotone voice? It means that your voice sounds like it doesn't vary in pitch, that it's on one note - vocally inexpressive.

What is monotone design?

Monotone means using only one colour. This is particularly used to mean black and white. Many photographers choose to work with black and white images. Removing colour means that the images rely fully on tone to describe light, shape and form.

What is opposite of monotone?

Opposite of lacking variety or excitement. break. difference. dissimilarity. excitement.

What is a flat tone of voice?

Monotone is a droning, unchanging tone. ... When someone speaks in a monotone, his voice is flat and boring — plus listeners don't know how the speaker is feeling when everything sounds the same.

Is a monotone voice attractive?

A study has found that men with a steady tone of voice had a significantly higher number of sexual partners. Men with monotone voices are more attractive to women, a study has suggested. Monotonous voices are associated with strength, power and confidence, researchers said.