the equation is valid

USAGE SUMMARY

The phrase "the equation is valid" is correct and usable in written English.
You can use it when discussing mathematical concepts or verifying the correctness of an equation in a mathematical context. Example: "After simplifying the terms, we can conclude that the equation is valid and holds true for all values of x."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

13 human-written examples

The equation is valid for laminar, mixed convection conditions in vertical, internal, aiding flows with constant wall temperature boundary condition.

International Journal of Heat and Fluid Flow

The equation is valid in the low frequency range where the sound wavelength is greater than the tube radius.

Journal of Sound and Vibration

The equation is valid for rectangular columns with doubly symmetric reinforcement and both normal and high strength concrete, and also for short-term and sustained loads.

Engineering Structures

The equation is valid in the bubbling regime up to transition to the jetting regime and for liquids with very low up to very high viscosities.

Chemical Engineering Science

The equation is valid for temperatures from the triple point to 460 K, and pressures up to 70 MPa, and it behaves in a qualitatively rational manner even in the region far from the range of existing experimental data.

Fluid Phase Equilibria

The equation is valid only for the Middle Bakken Formation.

Petroleum Science

Human-verified similar examples from authoritative sources

Similar Expressions

47 human-written examples

For sufficiently thick orifices, the equation was valid over a wide range of average porosities, from 0.3 to 0.6.

Journal of Wind Engineering and Industrial Aerodynamics

(iv) The inertial force due to the harmonic web oscillation with amplitude A and frequency f ; this equation is valid in the regime where the chips remain in contact with the web.

Advanced Materials

$$\end{document} This equation is valid for the entire range of carrier gas flow rates suitable for the MCC used.

Analytical and Bioanalytical Chemistry

The equations are valid in the neighbourhood of a steady state and may be useful in controling the reactor operation.

Chemical Engineering Science

The equations are valid for aqueous solutions saturated with hydrogen at low values of the Reynolds number.

Electrochimica Acta

Expert writing Tips

Best practice

When using "the equation is valid", always specify the conditions or limitations under which the equation holds true. This adds precision and avoids misinterpretations.

Common error

Avoid stating that "the equation is valid" without mentioning the specific context or conditions in which it applies. Equations often have limitations, and failing to acknowledge them can lead to incorrect applications.

Linguistic Context

The phrase "the equation is valid" functions as an assertion of truth or applicability. It's used to confirm that a mathematical relationship or formula yields correct results under specified conditions. Ludwig AI confirms this usage across varied contexts.

Expression frequency: Uncommon

Frequent in

Science

90%

Academia

5%

Wiki

3%

Less common in

News & Media

1%

Formal & Business

0%

Encyclopedias

0%

Ludwig's WRAP-UP

In summary, "the equation is valid" is a phrase used to affirm the accuracy and applicability of a mathematical equation under specific conditions. Ludwig AI indicates that it's grammatically correct and primarily used in formal and scientific contexts. The phrase is often followed by a specification of the conditions or limitations under which the equation holds true. While alternatives like "the equation holds" or "the equation is correct" exist, the choice depends on the desired nuance. Ensure that when using this phrase, you provide the necessary context to avoid misinterpretations and promote clarity.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

the equation holds

Replaces "is valid" with "holds", focusing on the equation's ability to maintain its truth.

the equation is correct

Substitutes "valid" with "correct", highlighting the equation's accuracy.

the equation is true

Emphasizes the verity of the equation.

the equation applies

Focuses on the applicability of the equation in a specific scenario.

the equation is applicable

Highlights the equation's suitability for a particular purpose.

the equation is satisfied

Indicates that the equation's conditions are met.

the equation stands

Suggests the equation's ability to withstand scrutiny or testing.

the equation remains true

Emphasizes the equation's enduring validity under certain circumstances.

the equation is verified

Highlights that the validity of the equation has been checked and confirmed.

the equation is confirmed

Similar to "verified", it indicates that the equation's validity has been firmly established.

FAQs

What does it mean when we say "the equation is valid"?

Saying "the equation is valid" means the equation is correct and produces accurate results under specific conditions or within a defined range of parameters. It implies that the relationship expressed by the equation holds true.

What are some alternatives to "the equation is valid"?

You can use alternatives such as "the equation holds", "the equation is correct", or "the equation applies" depending on the specific nuance you want to convey. For example, "the equation holds" emphasizes the maintenance of truth, while "the equation applies" focuses on its suitability in a given situation.

Is it more appropriate to say "the equation is valid" or "the equation is correct"?

Both phrases are acceptable, but "the equation is valid" often implies that the equation's correctness is conditional, while "the equation is correct" suggests a more general accuracy. The best choice depends on the context.

How do I specify the conditions under which "the equation is valid"?

You can specify the conditions by adding a phrase like "the equation is valid for...", followed by the specific conditions or limitations. For instance, "The equation is valid for laminar flow only" or "The equation is valid when certain assumptions are met".