uniform limit

USAGE SUMMARY

The phrase "uniform limit" is correct and usable in written English.
It is typically used in mathematical contexts, particularly in analysis, to describe a type of convergence of functions. Example: "The sequence of functions converges to a uniform limit, ensuring that the convergence is uniform across the entire interval."

✓ Grammatically correct

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

28 human-written examples

But the police said a uniform limit would allow them to write more speeding tickets, deterring speeders.

The New York Times

Consequently the uniform limit ; see [21, Lemma 2.5].

Boundary Value Problems

Let us denote by ψ ( t ) its relative uniform limit.

Advances in Difference Equations

Therefore the sequence for each, and hence its uniform limit.

Boundary Value Problems

Since is given by the uniform limit of the sequence, is also continuous on.

Advances in Difference Equations

Now in some neighborhood of we see that is the uniform limit of (3.3).

Journal of Inequalities and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

32 human-written examples

John Strand, a mobile industry analyst who specializes in such resellers, said the commission's proposal, by setting uniform limits on data roaming across the European Union, may have the unintended effect of squeezing out small companies that have already started to sell roaming packages.

The New York Times - Tech

The uniform limits in (3.4) are evident.

Advances in Difference Equations

This is impossible because we have the uniform limits (3.4).

Advances in Difference Equations

(i) Since, it follows from the uniform limits in (3.4) that (3.26)  .

Advances in Difference Equations

Since, it follows from the uniform limits in (3.4) that (3.26).

Advances in Difference Equations

Expert writing Tips

Best practice

When discussing convergence in mathematical analysis, specify the space or domain over which the "uniform limit" applies to ensure clarity and precision.

Common error

Avoid assuming that pointwise convergence implies uniform convergence. Pointwise convergence only requires convergence at each point individually, while "uniform limit" requires convergence at the same rate across the entire domain.

Linguistic Context

The phrase "uniform limit" primarily functions as a technical term within mathematical analysis. According to Ludwig AI, it's grammatically correct, describing a specific type of convergence where the limit is approached at the same rate across the entire domain, differentiating it from pointwise convergence. The provided examples showcase its use in scientific and mathematical contexts.

Expression frequency: Common

Frequent in

Science

70%

News & Media

15%

Encyclopedias

5%

Less common in

Formal & Business

5%

Wiki

0%

Reference

0%

Ludwig's WRAP-UP

The phrase "uniform limit" is a technical term primarily used in mathematics and scientific fields. According to Ludwig AI, it's grammatically sound and denotes a specific type of convergence that's consistent across an entire domain. While alternatives like "uniform convergence" exist, "uniform limit" is crucial in discussions where consistent approximation and stability are essential. As highlighted by the usage analysis, it appears most frequently in scientific contexts, but may appear in news. Remember to distinguish uniform from pointwise convergence for accuracy.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

uniform convergence

This alternative focuses on the process of approaching a limit consistently across a domain.

consistent limit

This highlights the consistency of the limit being approached.

even limit

This suggests an equal or balanced approach to the limit.

regular limit

This emphasizes the predictability and orderliness of the limit.

stable limit

This indicates a limit that does not fluctuate or vary.

steady-state limit

This emphasizes a limit that reaches a constant, unchanging state.

limit under uniform conditions

This specifies the conditions under which the limit is achieved.

limit with uniform properties

This highlights the characteristics that remain constant as the limit is approached.

homogenous limit

Implies the limit is the same throughout the domain.

equable limit

Suggests a fair and balanced approach to the limit.

FAQs

How is "uniform limit" used in mathematical analysis?

In mathematical analysis, "uniform limit" describes the limit of a sequence of functions that converges uniformly, meaning the convergence occurs at the same rate across the entire domain. This is a stronger condition than pointwise convergence.

What is the difference between pointwise convergence and "uniform limit"?

Pointwise convergence means a sequence of functions converges at each point in the domain, while a "uniform limit" requires the sequence to converge at the same rate across the entire domain. Uniform convergence implies pointwise convergence, but the converse is not always true.

When is it appropriate to use the term "uniform convergence" instead of "uniform limit"?

"Uniform convergence" refers to the property of a sequence of functions, while "uniform limit" refers to the actual limit function that results from this type of convergence. They are related but describe different aspects of the same phenomenon. They can be used interchangeably.

What are some practical examples where understanding "uniform limit" is crucial?

Understanding "uniform limit" is crucial in areas like differential equations, where the convergence of solutions needs to be consistent across a domain, and in approximation theory, where the accuracy of approximations needs to be uniformly controlled. Also, you can consider using "consistent limit".