decreasing sequence

USAGE SUMMARY

The phrase "decreasing sequence" is correct and usable in written English.
It can be used in mathematical contexts to describe a sequence of numbers where each term is less than or equal to the preceding term. Example: "In this problem, we need to find the sum of the first five terms of the decreasing sequence: 10, 8, 6, 4, 2."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

58 human-written examples

Given any increment of time, the distances traveled by the first particle in successive increments form a geometrically decreasing sequence.

Britannica

The residue of different samples was in decreasing sequence as lignin > pectin > hemicellulose > starch > cellulose.

Fuel

Let be a strictly decreasing sequence in.

Fixed Point Theory and Applications

where is a strictly decreasing sequence in and set.

Fixed Point Theory and Applications

Let x n be an increasing or decreasing sequence.

Journal of Inequalities and Applications

Since is a strictly decreasing sequence and, we have.

Journal of Inequalities and Applications

If is a decreasing sequence converging to, then (3.14).

Fixed Point Theory and Applications

Every bounded decreasing sequence in Y is convergent.

Fixed Point Theory and Applications

Let with be a strictly decreasing sequence, and with.

Fixed Point Theory and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

2 human-written examples

Given a non-decreasing sequence of non-negative integers, is it the score list of some tournament?

University of California, Berkeley

and hence { x n } is a non-decreasing sequence.

Fixed Point Theory and Applications

Expert writing Tips

Best practice

When describing a "decreasing sequence", be precise about whether the sequence is strictly decreasing (each term is less than the previous) or non-increasing (each term is less than or equal to the previous).

Common error

A common mistake is assuming a "decreasing sequence" must involve negative numbers. A sequence can decrease from positive values toward zero or even a positive limit, without any negative terms.

Linguistic Context

The phrase "decreasing sequence" functions as a noun phrase, primarily used to describe a series of numbers or values that diminish in magnitude over successive terms. Ludwig provides numerous examples in scientific and mathematical contexts, confirming its descriptive role.

Expression frequency: Very common

Frequent in

Science

95%

Encyclopedias

2%

Academia

1%

Less common in

News & Media

0%

Formal & Business

0%

Wiki

0%

Ludwig's WRAP-UP

The term "decreasing sequence" is widely recognized and accepted as grammatically correct, according to Ludwig. It is frequently encountered in scientific and mathematical contexts to describe ordered sets of numbers that diminish over time. When using this phrase, it's important to clarify whether the sequence is strictly decreasing or simply non-increasing. While the phrase is accurate, alternatives such as "monotonically decreasing sequence" or "descending sequence" can add nuance depending on the specific context. A key point to remember is that a "decreasing sequence" does not necessarily involve negative numbers; it simply requires a consistent diminishing trend.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

monotonically decreasing sequence

Emphasizes the consistent and non-increasing nature of the sequence.

strictly decreasing sequence

Indicates that each term is strictly less than the preceding term.

descending sequence

A more general term for a sequence where the values go down.

decreasing progression

Uses "progression" to highlight the ordered and sequential nature.

convergent decreasing sequence

Adds the condition that the sequence approaches a limit.

sequence approaching zero

Specifically indicates that the sequence diminishes toward zero.

sequence tending to zero

Similar to 'sequence approaching zero', but emphasizes the trend.

diminishing sequence

Highlights the diminishing nature of the terms in the sequence.

non-increasing sequence

A sequence where the terms are not increasing, allowing for constant values.

sequence with a negative trend

Describes the sequence in terms of its trend or direction.

FAQs

What is a real-world example of a "decreasing sequence"?

A simple example is the amount of water remaining in a leaking bucket over time, assuming no water is added. The amount decreases continuously, forming a "decreasing sequence".

What is the difference between a "decreasing sequence" and a "strictly decreasing sequence"?

A "decreasing sequence" allows for terms to be equal to the previous term (non-increasing), while a "strictly decreasing sequence" requires each term to be strictly less than the previous term.

When is it appropriate to use the term "decreasing sequence"?

The term "decreasing sequence" is appropriate in mathematical analysis, computer science algorithms, and any field where ordered sets of numbers or values diminish over iterations or steps.

Are there alternatives to the term "decreasing sequence"?

Yes, depending on the context, you can use "descending sequence", "non-increasing sequence", or even describe the sequence as "monotonically decreasing".