all possible solutions of

USAGE SUMMARY

The phrase "all possible solutions of" is correct and usable in written English.
It can be used in contexts such as mathematics, problem-solving, or discussions about options and alternatives. Example: "We need to consider all possible solutions of the equation before making a decision."

✓ Grammatically correct

Science

News & Media

Computers & Structures

Automatica

Human-verified examples from authoritative sources

Exact Expressions

14 human-written examples

The algorithm for constructing the general solution (the set of all possible solutions) of the problem is proposed.

Computers & Structures

For several applications, the guaranteed enclosure of all possible solutions of an initial value problem (IVP) of a given uncertain system is demanded.

IFAC Proceedings Volumes

The design of the event-triggered control is based on two conditions: one to solve the event-triggered control co-design for LQ stabilization; the second one to adjust the co-design among all possible solutions of the first condition thanks to a tunable parameter.

Automatica

We claim that there exists, independent of and, such that for all possible solutions of (3.36).

Advances in Difference Equations

We first prove that the set of all possible solutions of problem (3.1 - 3.2 3.1 - 3.2ed.

Boundary Value Problems

A compact map or homotopy is constructed enabling us to show that if there is an a priori bound on all possible solutions of the companion control system, then there exists a solution for.

Fixed Point Theory and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

46 human-written examples

Now d loops over all directed paths in D. In other words, d loops over all possible solutions for the head of the route e, constituted by candidates of the currently considered subset S.

European Transport Research Review

The search space of a problem, i.e., the space of all possible solutions to the problem, is investigated by applying a set of optimization techniques that imitate the theory of evolution, combining natural selection and genetic operations, to create more diverse and better performing individuals in subsequent generations to provide a way to find near-optimal solutions for a given task.

Journal of the Brazilian Computer Society

It is an abbreviation of trade-off space, which is a graphical representation and database of supporting data and mathematical models of all possible solutions to an evaluation problem.

Journal of Modern Transportation

The phylogenetic network shown in Figure 5 shows a consensus of all possible solutions to the phylogenetic tree, emphasising the various, and equally plausible, ways of depicting isoform relationships.

BMC Genomics

The idea of this stage is simulation and good representation of all possible solutions for the next stage.

Journal of Industrial Engineering International

Expert writing Tips

Best practice

When discussing mathematical or logical problems, use "all possible solutions of" to ensure the consideration of every potential outcome.

Common error

Ensure that when you say "all possible solutions of", you've defined the scope and constraints of the problem clearly. Otherwise, the phrase becomes too broad and unhelpful.

Linguistic Context

The phrase "all possible solutions of" functions as a noun phrase, typically acting as the object of a verb or preposition. It identifies the entire set of potential resolutions to a problem or equation. As evidenced by Ludwig, it's commonly used in scientific and technical writing.

Expression frequency: Common

Frequent in

Science

70%

News & Media

10%

Formal & Business

10%

Less common in

Encyclopedias

3%

Wiki

3%

Academia

4%

Ludwig's WRAP-UP

In summary, the phrase "all possible solutions of" is a grammatically sound and commonly used expression to denote a comprehensive range of potential resolutions to a problem. Ludwig highlights its frequent application in science, technology, and mathematics contexts. Its function is to explore and enumerate all options, indicating a formal and scientific register. When using this phrase, ensure the scope of the problem is clearly defined to avoid ambiguity. Consider alternatives like "every potential solution of" or "the complete set of solutions for" depending on the context. Remember that while it is essential to consider "all possible solutions of", the final goal is to choose the most effective one.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

every potential solution of

Replaces "possible" with "potential", suggesting a focus on solutions that could exist or become real.

the complete set of solutions for

Emphasizes the exhaustive nature of the solutions and specifies that it is a "complete set".

the entirety of solutions for

Uses "entirety" instead of "complete set", emphasizing a full range of solutions.

every conceivable solution to

Replaces "possible" with "conceivable", highlighting the range of imaginable solutions.

the universe of solutions for

Uses "universe" to denote the vastness and comprehensiveness of the solutions.

all viable solutions to

Substitutes "possible" with "viable", focusing on solutions that are practical and workable.

the full spectrum of solutions for

Uses "full spectrum" to suggest a wide range of solutions from different perspectives.

a complete range of solutions for

Uses the word 'range' instead of 'set', focusing on a variety of all available options.

every feasible solution of

The adjective 'feasible' replaces 'possible' suggesting solutions that are realistically achievable.

the exhaustive listing of solutions to

Focuses on providing a comprehensive and thorough list of all solutions.

FAQs

How can I rephrase "all possible solutions of"?

You can use alternatives like "every potential solution of", "the complete set of solutions for", or "every conceivable solution to" depending on the context and desired emphasis.

When is it appropriate to use the phrase "all possible solutions of"?

Use "all possible solutions of" when you need to consider every potential answer or outcome to a problem, ensuring no solution is overlooked. This is common in math, science, and problem-solving contexts.

What is the difference between "all possible solutions of" and "the best solution of"?

"All possible solutions of" refers to the complete set of potential answers, while "the best solution of" refers to the single, most optimal answer chosen from those possibilities.

Is it more formal to say "all potential solutions of" instead of "all possible solutions of"?

The phrase "all potential solutions of" is slightly more formal than "all possible solutions of", but both are appropriate for academic and professional contexts.