least solutions

USAGE SUMMARY

The phrase "least solutions" is not correct and does not convey a clear meaning in written English.
It may be intended to refer to the smallest or minimal number of solutions, but the phrasing is awkward and unclear. Example: "In this problem, we need to find the least solutions that satisfy all conditions."

⚠ May contain grammatical issues

Science

Human-verified examples from authoritative sources

Exact Expressions

2 human-written examples

In general, in the conditions of Theorem 1 we cannot expect problem (1) to have the extremal solutions in (that is, the greatest and the least solutions in ).

Boundary Value Problems

The first result ensures the existence of maximal and minimal solutions, and the second one establishes the existence of the greatest and the least solutions in a particular case.

Boundary Value Problems

Human-verified similar examples from authoritative sources

Similar Expressions

58 human-written examples

Moreover the least solution of (1.1) in is given by (3.3).

Boundary Value Problems

Claim 3. is the least solution of (1.1) in and is the greatest one.

Boundary Value Problems

In an analogous way we obtain the least solution of the problem in ([alpha,beta]).

Boundary Value Problems

Thus, (1.1) has at least four solutions.

Journal of Inequalities and Applications

Hence, (1.1) has at least five solutions.

Boundary Value Problems

Then, (1.1) has at least eight solutions.

Boundary Value Problems

At least two solutions to this problem have been formulated.

SEP

By Theorem 3.1, (3.13) has at least eight solutions.

Boundary Value Problems

By Theorem 3.3, problem (3.11) has at least two solutions.

Advances in Difference Equations

Expert writing Tips

Best practice

When referring to the smallest number of solutions, use "fewest solutions" or "minimum number of solutions" for clarity. When referring to the smallest solution, use "least solution".

Common error

Avoid using "least solutions" when you mean "at least some solutions". The former implies a minimum set of solutions, while the latter simply indicates the existence of one or more solutions.

Linguistic Context

The phrase "least solutions" attempts to describe the minimum number of solutions to a problem. However, it's not standard English. The more appropriate term in most mathematical and technical contexts would be "fewest solutions" or "minimum number of solutions". Ludwig AI indicates the phrase is not entirely correct.

Expression frequency: Rare

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Science

0%

Ludwig's WRAP-UP

The phrase "least solutions" is not grammatically correct, according to Ludwig AI, and should be used with caution. While the intention is generally to refer to the minimum number of solutions to a problem, clearer and more precise alternatives like "fewest solutions" or "minimum number of solutions" are preferred. Context is key; the term "least solution" has a specialized meaning in math. When describing that there is a minimum of one solution, use the phrase "at least one solution". While sources are authoritative, the non-standard nature of "least solutions" means writers must strive for clarity and precision in technical and mathematical writing. Given this, the use of the phrase should be reconsidered in favour of other alternatives. Most of the sources categorized in Ludwig belong to the Science category.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

fewest solutions

Focuses on the minimal quantity of solutions required.

minimum number of solutions

Specifies the smallest acceptable count of solutions.

minimal solutions

Emphasizes the solutions that are, in some sense, the 'smallest' or 'simplest'.

smallest solutions

Refers to solutions with the lowest numerical value or magnitude.

lowest-value solutions

Highlights the solutions that result in the smallest outcome.

at least one solution

Indicates the existence of one or more solutions, establishing a lower bound.

optimal solutions

Highlights solutions that satisfy an optimality criterion.

least complex solutions

Emphasizes the simplicity and ease of calculation and implementation of solutions.

least resource-intensive solutions

Highlights the solutions with the lowest usage of resources.

at a minimum number of solutions

Specifies the lowest acceptable count of solutions.

FAQs

How to correctly use the term "least solution"?

The term "least solution" is used in mathematics to refer to the smallest solution to a problem. For example, it could mean the smallest value that satisfies an equation. It is very specific.

What is a better way to refer to a small quantity of solutions?

Instead of "least solutions", consider using alternatives such as "fewest solutions" or "minimum number of solutions" to clearly indicate you're referring to the smallest possible quantity.

Is it grammatically correct to say "least solutions"?

While understandable, "least solutions" is not grammatically ideal. "Fewest solutions" or "minimum number of solutions" are clearer and more precise.

When should I use "at least one solution" instead of "least solutions"?

Use "at least one solution" when you want to express that there is a minimum of one solution, but there could be more. "Least solutions" doesn't convey this meaning effectively and is usually not the intended phrase.