equation holds

USAGE SUMMARY

"equation holds" is correct and usable in written English.
You can use it when referring to the fact that an equation is true. For example: "After running the calculations, it was determined that the equation holds."

✓ Grammatically correct

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

57 human-written examples

In detail, for we additionally have to analyze for case if the equation holds and for case, if and are valid.

EURASIP Journal on Embedded Systems

For small driving forces in dilute systems the equation holds.

Chemical Engineering Science

Still the equation holds — jobs and health and schools and better than before and different from now and enough and always and eventually mine.

The New Yorker

The Nernst equation holds in the Ag+ concentration range of 10−3 −5 × 10−1 mol kg.

Electrochimica Acta

In vitro/in vivo correlation was tested based on the hypothesis that the same linear regression equation holds for three formulations with different release rates.

Journal of Pharmaceutical Sciences

In particular, it is shown that there exists a range of the material parameters where the standard 1D diffusion equation holds.

International Journal of Solids and Structures

The above equation holds because.

EURASIP Journal on Wireless Communications and Networking

The following equation holds: (3.12).

Journal of Inequalities and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

3 human-written examples

If we want to compare PER performance as the function of average signal power to the average noise power ratio (SNR), the following equation holds [19]: (26).

EURASIP Journal on Advances in Signal Processing

Now, Mr. Gingrich will get to see if the other side of the equation holds up — that, alone, he could rally an anti-Romney vote, though that seems far-fetched.

The New York Times

Considering the even power allocation, e.g., P i = P J N, ∀ i, the following equation holds β i β j = q i E q j E. (24).

EURASIP Journal on Wireless Communications and Networking

Expert writing Tips

Best practice

When using "equation holds", ensure that the context clearly defines the variables and conditions under which the equation is valid. Specify any assumptions or limitations that apply.

Common error

Avoid assuming that an equation holds universally without specifying the necessary constraints or boundary conditions. Always clarify the scope of applicability to prevent misinterpretations.

Linguistic Context

The phrase "equation holds" functions as a statement asserting the validity or truth of a mathematical equation within a specific context. As Ludwig AI confirms, this is a correct and usable expression. Examples show its frequent use in scientific and mathematical contexts.

Expression frequency: Very common

Frequent in

Science

90%

News & Media

5%

Formal & Business

5%

Less common in

Encyclopedias

0%

Wiki

0%

Social Media

0%

Ludwig's WRAP-UP

The phrase "equation holds" is a common expression, primarily used in scientific and mathematical contexts, to assert the validity of an equation under certain conditions. As Ludwig AI highlights, this phrase is grammatically correct and widely accepted. It's crucial to specify the context and any limitations to avoid misinterpretations. When looking for alternatives, consider phrases like "equation is valid" or "equation is true" for similar meanings. Remember to always clarify the scope to ensure precise communication.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

the equation is valid

Replaces "holds" with "is valid", emphasizing the truthfulness of the equation.

the equation is true

Substitutes "holds" for "is true", directly asserting the equation's correctness.

the equation is satisfied

Employs "is satisfied" instead of "holds", indicating that the equation's conditions are met.

the equation stands

Uses "stands" in place of "holds", suggesting the equation remains correct under scrutiny.

the equation remains valid

Replaces "holds" with "remains valid", indicating continued correctness.

the equation applies

Substitutes "holds" with "applies", focusing on the equation's relevance in a context.

the equation is correct

Directly asserts that the equation "is correct" instead of stating that it holds.

the equation is fulfilled

Employs "is fulfilled" to show that the equation's condition is met, instead of stating that it holds.

the equality holds

Replaces "equation" with "equality", which may be more appropriate in some contexts, keeping "holds".

the relation holds

Substitutes "equation" with "relation", which may broaden the scope, keeping "holds".

FAQs

How can I use "equation holds" in a sentence?

You can use "equation holds" to state that an equation is true or valid under certain conditions. For example: "The equation holds true when x is greater than zero."

What does it mean when an equation "holds"?

When an equation "holds", it means that the equation is true or valid given the specified conditions. It indicates that the equality or relationship expressed by the equation is correct.

Which is correct, "equation holds" or "equation is held"?

"Equation holds" is the correct phrasing. "Equation is held" isn't standard usage. You might consider alternatives like "equation is valid".

What are some alternative ways to say "equation holds"?

You can use alternatives such as "equation is true", "equation is valid", or "equation is satisfied" depending on the specific nuance you want to convey.