convergent to

USAGE SUMMARY

The phrase "convergent to" is correct and usable in written English.
It is typically used in mathematical or scientific contexts to describe a sequence or series that approaches a specific value or limit. Example: "As n approaches infinity, the sequence is convergent to the limit of 5."

✓ Grammatically correct

Science

Encyclopedias

Human-verified examples from authoritative sources

Exact Expressions

46 human-written examples

The contour is initially convergent to a "throat" section.

Encyclopedia Britannica

convergent to if the set is -null.

Fixed Point Theory and Applications

The sequence is convergent to in.

Boundary Value Problems

Such series are uniformly convergent to the exact solution.

Journal of Sound and Vibration

Then x is statistically convergent to 0 but not convergent.

Journal of Inequalities and Applications

Let a sequence such that is weakly convergent to.

Journal of Inequalities and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

14 human-written examples

Let { f n } in F ( F ) ρ-convergent to f.

Fixed Point Theory and Applications

Clearly, this net is supra-convergent to (x_{o}).

Boundary Value Problems

Therefore, (g(gx n )) is G-convergent to gx and (g gy n )) is G-convergent to gy.

Fixed Point Theory and Applications

Since g is G-continuous, we have { g g x n } is G-convergent to gx and { g g y n } is G-convergent to gy.

Fixed Point Theory and Applications

This shows that { x n } is Δ-convergent to a point of F ( S, T ).

Journal of Inequalities and Applications

Expert writing Tips

Best practice

When discussing mathematical sequences or iterative processes, use "convergent to" to clearly indicate the limit the sequence is approaching. For instance, "The algorithm's output is convergent to the optimal solution."

Common error

Avoid using "convergent to" in contexts where a more general term like "approaching" or "tending toward" would be more appropriate. "Convergent to" is most precise in contexts involving limits and mathematical progressions, it should not be used in general contexts like "Their opinions are convergent to mine".

Linguistic Context

The phrase "convergent to" primarily functions as a verb phrase complement, describing the state of approaching a limit or a specific value. As Ludwig AI confirms, this usage is grammatically correct and prevalent in scientific and mathematical contexts.

Expression frequency: Common

Frequent in

Science

70%

Encyclopedias

15%

Formal & Business

5%

Less common in

News & Media

3%

Wiki

2%

Reference

5%

Ludwig's WRAP-UP

In summary, the phrase "convergent to" is a grammatically correct and commonly used term, especially in scientific and mathematical contexts. Ludwig AI provides numerous examples highlighting its function in describing sequences or processes approaching a specific limit or value. While alternatives like "approaching" or "tending toward" exist, "convergent to" offers precision in mathematical and scientific discussions. The phrase maintains a formal register, as evidenced by its prevalence in academic and scientific sources. As confirmed by Ludwig AI, understanding the appropriate context is crucial for effective usage, avoiding more general terms when precision is necessary.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

approaching

Implies movement closer to a target or value; broader in scope.

tending toward

Suggests an inclination or direction towards something; less formal.

moving towards

Emphasizes the dynamic process of approaching a value or state.

heading for

Indicates a specific destination or outcome being approached.

aiming at

Suggests a deliberate intention to reach a certain value or target.

closing in on

Implies reducing the distance to a target; can suggest urgency.

gravitating toward

Suggests attraction or influence leading towards a state.

drifting towards

Implies a slow, gradual movement in a specific direction.

becoming similar to

Focuses on increasing resemblance or likeness over time.

leveling off at

Indicates that a previously increasing/decreasing function becomes stable near a certain value

FAQs

How to use "convergent to" in a sentence?

Use "convergent to" to describe a sequence, series, or process that approaches a specific value or limit. For example, "The iterative process is "convergent to" the solution."

What can I say instead of "convergent to"?

You can use alternatives like "approaching", "tending toward", or "moving towards" depending on the context. "converging on" might also work.

Is it correct to say "convergent at" instead of "convergent to"?

No, the correct preposition to use with "convergent" in this context is "to". "Convergent at" is not standard usage. Use ""convergent to"" to indicate the value or limit being approached.

What's the difference between "convergent to" and "converging on"?

"Convergent to" implies a mathematical or process-oriented approach toward a specific value, while "converging on" suggests a more general process of coming together or focusing on a particular point or area.