equivalent solutions

USAGE SUMMARY

The phrase "equivalent solutions" is correct and usable in written English.
It can be used in contexts where you are discussing different methods or answers that achieve the same result or outcome. Example: "In our analysis, we found that both methods provided equivalent solutions to the problem at hand."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

35 human-written examples

The underlying principle is that equivalent problems have equivalent solutions.

SEP

The optimization algorithm has conducted to a set of equivalent solutions named Pareto optimal set.

Chemical Engineering Research and Design

There are problems however for which several sets of constants represent valid equivalent solutions.

EURASIP Journal on Embedded Systems

Such an approach appears more effective than other traditional inversion methods because it allows to calculate exhaustively a probabilistic description of the equivalent solutions.

Journal of Applied Geophysics

The inherent non-uniqueness of this inverse problem and the errors in the residual gravity data lead to the existence of equivalent solutions.

Earth, Planets and Space

In fact, all the above mentioned predictor weights deliver identical values for the cross-validation criterion, thus they are all equivalent solutions of the cross-validation approach.

Swiss Journal of Economics and Statistics

Human-verified similar examples from authoritative sources

Similar Expressions

25 human-written examples

While you may be able to build an equivalent solution using non-Microsoft technologies, your ability to maintain it over the long-haul is a question worth asking.

Forbes

Diffeomorphism invariance means, informally, that one can take a solution of Einstein's equations and drag it (meaning the metric and the matter fields) around on the spacetime manifold and obtain a mathematically distinct but physically equivalent solution.

SEP

To decode the list presented in Figure2 and obtain its equivalent solution in the solution space, we start from the beginning of the list and schedule the first operation.

Journal of Industrial Engineering International

Such integral presentation of the derivative of reciprocal gamma function, and also HC is known, but the equivalent solution (3.1) is not explained enough with the alternative members of the psi functions.

Advances in Difference Equations

If the MSER precoder matrix has equal elements, it can be shown that there exists an equivalent solution (which is also optimal in the MSER sense) of the form (see Appendix E): (39).

EURASIP Journal on Wireless Communications and Networking

Expert writing Tips

Best practice

When discussing multiple approaches that lead to the same outcome, use "equivalent solutions" to highlight that each method is equally valid. Be specific about what makes them equivalent, such as performance, cost, or ease of implementation.

Common error

Avoid using "equivalent solutions" in everyday conversation where simpler terms like "alternatives" or "same thing" would suffice. The phrase is best suited for technical or scientific discussions where precision is valued.

Linguistic Context

The phrase "equivalent solutions" functions as a noun phrase, typically used as the object of a verb or preposition. It refers to multiple answers or approaches that are considered functionally identical in achieving a specific outcome. Ludwig AI validates its correct usage across various domains.

Expression frequency: Common

Frequent in

Science

94%

News & Media

6%

Formal & Business

0%

Less common in

Encyclopedias

0%

Wiki

0%

Reference

0%

Ludwig's WRAP-UP

In summary, the phrase "equivalent solutions" is grammatically sound and commonly used, particularly in scientific and technical domains. As Ludwig AI confirms, its primary function is to describe multiple approaches that yield the same result, implying that these options are functionally identical. When writing, using more common terms like "alternatives" or "same thing" may be more suitable to avoid being perceived as overly formal or technical in some context. However, in formal writing such as scientific papers, the phrase is perfectly appropriate and useful.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

identical solutions

Focuses on the solutions being exactly the same, emphasizing a complete match.

interchangeable solutions

Highlights the ability to use the solutions in place of each other without affecting the outcome.

commutable solutions

Emphasizes the property of the solutions that their order of application does not affect the final result.

equal solutions

A more straightforward way of saying the solutions have the same value or result.

alternative solutions

Indicates that the solutions provide a different way to achieve the same end.

corresponding solutions

Suggests that solutions match each other in a specific context or problem.

parallel solutions

Implies solutions that are developed or applied alongside each other to achieve a similar goal.

analogous solutions

Highlights a similarity in function or effect between the solutions.

comparable solutions

Stresses the similarity of solutions when assessed against a set of criteria.

matching solutions

Indicates that solutions are similar or identical with respect to certain qualities.

FAQs

How can I use "equivalent solutions" in a sentence?

You can use "equivalent solutions" to describe different methods or approaches that yield the same result. For example: "We found several "interchangeable solutions" to this problem, all of which offer similar performance characteristics."

What's the difference between "equivalent solutions" and "similar solutions"?

"Equivalent solutions" implies that the results are functionally the same, whereas "similar solutions" suggests that the results are alike but not necessarily identical. The choice depends on the degree of precision you wish to convey.

What can I say instead of "equivalent solutions"?

Depending on the context, you can use alternatives like "identical solutions", "alternative solutions", or "comparable solutions".

Is it appropriate to use "equivalent solutions" in formal writing?

Yes, "equivalent solutions" is perfectly appropriate in formal and technical writing, especially in scientific, engineering, or mathematical contexts where precise language is important.