are tending to zero

USAGE SUMMARY

The phrase "are tending to zero" is correct and usable in written English.
It can be used in mathematical or scientific contexts to describe a quantity that is approaching zero over time or under certain conditions. Example: "As the temperature decreases, the energy levels of the particles are tending to zero."

✓ Grammatically correct

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

3 human-written examples

Following [2, 5], we prove that all solutions of the problem (1.4)–(1.6) are tending to zero with a polynomial rate as.

Journal of Inequalities and Applications

It is shown that the zero solution of the problem (1.3 - 1.2) is globally asymptotically stable, that is, the zero solution is stable and all solutions of this problem are tending to zero when.

Journal of Inequalities and Applications

In particular, we consider the asymptotic stable case, when the solutions x ( n ) of (2.1) are tending to zero as n → ∞, and describe the exact rate of their decay.

Advances in Difference Equations

Human-verified similar examples from authoritative sources

Similar Expressions

57 human-written examples

These days, they are tending to two youngsters, ages 4 and 6; fields of vegetables; and a pomegranate orchard in the mountains.

Los Angeles Times

Consequently, the frequency of their appearance is increasing and the distances between their ordinates is tending to zero as.

Journal of Inequalities and Applications

A key property discussed in connection with (2.2) and (2.3) is their asymptotic stability; more precisely, a formulation of necessary and sufficient conditions guaranteeing that any solution y is tending to zero as t → ∞.

Advances in Difference Equations

Whereas Mitchell says she is at her best dividing her time between two critically ill patients, she more often is tending to three or four.

The New York Times - Magazine

It traces back to 1975, when the Rev. Sean Brady, now a cardinal at the head of the Catholic Church in Ireland, was tending to two boys who had been molested by a priest.

The New York Times

Back in 2008, Mark Covington was tending to three vacant lots on his block when he decided to plant a community garden to stop people from illegally dumping their trash.

Huffington Post

Hence, the problem requires that the Eckert number Ec is assumed to be very small, that is, tends to zero.

International Nano Letters

And I had been tending to it for six hours!

BBC

Expert writing Tips

Best practice

In scientific writing, use "are tending to zero" to describe quantities that approach zero under specific conditions, such as in asymptotic analysis or when discussing limits.

Common error

Avoid using "are tending to zero" in everyday language. It's best suited for technical or scientific contexts where precise mathematical behavior is being described.

Linguistic Context

The phrase "are tending to zero" functions as a verb phrase indicating a dynamic process where certain values or quantities approach zero. It's commonly used in mathematical and scientific contexts as indicated by Ludwig.

Expression frequency: Uncommon

Frequent in

Science

60%

News & Media

30%

Wiki

10%

Less common in

Formal & Business

0%

Encyclopedias

0%

Reference

0%

Ludwig's WRAP-UP

In summary, the phrase "are tending to zero" is a grammatically sound verb phrase used primarily within scientific and mathematical domains to express a progressive decrease towards zero. As Ludwig AI validates, it's most suitable for formal contexts requiring precision. While alternatives like "are approaching zero" exist, "are tending to zero" precisely describes asymptotic behavior in mathematical models. It is important to reserve its usage for contexts where this mathematical precision is needed.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

are approaching zero

Focuses on the action of approaching a value, emphasizing the movement towards zero.

are converging to zero

Implies a more mathematical and precise movement towards a limit of zero.

are diminishing to zero

Highlights the gradual decrease in value until it reaches zero.

are decreasing to zero

Emphasizes the process of reduction and eventual nullification.

are nearing zero

Focuses on the proximity to zero, suggesting the value is close to being zero.

are moving towards zero

Suggests directionality towards zero, highlighting the progression.

are declining to zero

Indicates a downward trend culminating in zero.

are falling to zero

Implies a rapid or uncontrolled descent to zero.

are dropping to zero

Conveys a quick and possibly abrupt decrease to zero.

are vanishing

Suggests a disappearance or complete elimination, implying a trend towards zero.

FAQs

How is "are tending to zero" used in mathematical contexts?

In mathematics, "are tending to zero" describes sequences or functions whose values approach zero as the index or variable approaches a certain limit. For instance, terms in a convergent series "converge to zero".

When is it appropriate to use "are tending to zero" in scientific writing?

Use "are tending to zero" to accurately describe quantities that diminish and approach zero, particularly in physics or engineering, when analyzing asymptotic behavior or stability of systems. For example, "dampened oscillations "decay to zero"".

What are some alternative phrases for "are tending to zero"?

Alternatives include "are approaching zero", "are converging to zero", or "are vanishing", depending on the specific nuance you wish to convey.

Is "are tending to zero" formal or informal language?

"Are tending to zero" is generally considered formal language, most appropriate for technical, mathematical, or scientific discussions. Using simpler terms like "are decreasing" might be better in informal contexts.