cannot be approximated

USAGE SUMMARY

The phrase "cannot be approximated" is correct and usable in written English.
It can be used in contexts where something is described as being impossible to estimate or represent closely. Example: "The value of pi is an irrational number, which means it cannot be approximated by a simple fraction."

✓ Grammatically correct

Science

Academia

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

- Proof 1 (Razborov-Smolensky): PARITY cannot be approximated by a low-degree polynomial (section 13.2).

Princeton University

This means that this problem cannot be approximated by a single schedule.

Journal of Parallel and Distributed Computing

Some other solutions, obtained numerically, cannot be approximated by conventional asymptotic methods.

Journal of Sound and Vibration

Yet many important practical systems are in the turbulent regime and cannot be approximated by a simplified analysis.

Progress in Energy and Combustion Science

This method is particularly suitable for determining the irregular profiles that cannot be approximated by the polynomial functions.

International Journal of Heat and Mass Transfer

It is shown that in this case these characteristics cannot be approximated by Newman's and other conventional formulate.

Electrochimica Acta

We show examples of compact linear operators between Banach spaces which cannot be approximated by norm attaining operators.

Journal of Functional Analysis

The shape of measured or design life distributions of systems can vary considerably, and therefore frequently cannot be approximated by simple distribution functions.

Reliability Engineering & System Safety

Considering synergistic valuations turns the allocation problem into a computationally hard optimization problem that generally cannot be approximated to a constant factor in polynomial time.

Telecommunications Policy

This implies that the trajectory of a celestial body whose mass is continuously changing cannot be approximated by a series of Keplerian orbits.

Advances in Space Research

Further, it is found that the flame centerlines cannot be approximated as one-dimensional, since the mass flow rates vary substantially along the centerlines.

Combustion and Flame

Expert writing Tips

Best practice

When using "cannot be approximated", ensure the context clearly explains why an approximation is not possible or suitable. Be specific about the limitations or complexities involved.

Common error

Avoid using "cannot be approximated" when a rough estimate or simplified model is still useful, even if not perfectly accurate. Consider whether "can be poorly approximated" or "difficult to approximate" might be more appropriate.

Linguistic Context

The phrase "cannot be approximated" functions as a passive construction, indicating the inability to estimate or represent something closely. Ludwig confirms its correct usage across various contexts.

Expression frequency: Very common

Frequent in

Science

78%

Academia

15%

News & Media

2%

Less common in

Formal & Business

2%

Encyclopedias

1%

Reference

1%

Ludwig's WRAP-UP

The phrase "cannot be approximated" is a grammatically sound and frequently used expression, particularly within scientific and academic domains. As Ludwig AI confirms, it serves to indicate the impossibility of accurately estimating or representing something, often due to inherent complexities or limitations. While versatile, its formal tone makes it most suitable for technical or academic discourse. When using "cannot be approximated", clarity and specificity are crucial to convey the rationale behind the impossibility of approximation.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

cannot be precisely determined

Emphasizes the lack of precision in determining a value or quantity.

cannot be accurately estimated

Focuses on the inability to make an accurate estimate.

cannot be closely replicated

Highlights the difficulty in creating a near-identical copy or model.

cannot be faithfully reproduced

Underscores the challenges in reproducing something with high fidelity.

cannot be readily simplified

Indicates the impossibility of simplifying a complex concept or system.

cannot be easily modeled

Focuses on the difficulty in creating a model that accurately represents something.

defies accurate representation

Highlights a complete failure for precise representation

is not amenable to approximation

Highlights the unsuitability for approximation

is beyond the scope of approximation

Highlights an approximation completely out of the scope

cannot be rendered exactly

Highlights an impossibility of rendering exactly something

FAQs

How can I use "cannot be approximated" in a sentence?

Use "cannot be approximated" when you want to express that something's true value or form is impossible to estimate or represent closely. For example, "Due to the chaotic nature of the system, its long-term behavior "cannot be approximated" with any degree of certainty."

What are some alternatives to "cannot be approximated"?

Alternatives include "cannot be precisely determined", "cannot be accurately estimated", or "defies accurate representation", depending on the nuance you want to convey. For example, in some cases, "cannot be estimated" is more appropriate.

Is it correct to say "cannot be closely approximated"?

While grammatically correct, "cannot be closely approximated" might be redundant. "Cannot be approximated" already implies a lack of closeness. Consider whether emphasizing the degree of approximation is necessary.

In what fields is the phrase "cannot be approximated" commonly used?

The phrase "cannot be approximated" is frequently used in technical fields such as mathematics, physics, engineering, and computer science where precision is important and some phenomena are too complex for simplification.