the equation implies that

USAGE SUMMARY

The phrase "the equation implies that" is correct and usable in written English.
You can use it when discussing mathematical or logical conclusions drawn from a given equation or statement. Example: "In this case, the equation implies that the total cost will increase as the number of units sold rises."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

8 human-written examples

The mappings and are weakly compatible if they commute at coincidence points, that is, for each point such that, then (note that the equation implies that is a singleton).

Fixed Point Theory and Applications

The equation implies that a relative change in the molar volume (ΔV/V) of the metal leads to a change in the plateau pressure according to Eq. (3), provided that the volume compression is elastic, hence remains intact upon hydrogenation of the metal.

Nature

This together with the equation implies that (2.20).

Boundary Value Problems

It is expected that the diffusive nature of the equation implies that the solution goes to zero when t → + ∞.

Boundary Value Problems

The periodicity of the equation implies that x(n + p; φ) is likewise a solution of the equation defined for n + p ≥ d.

Advances in Difference Equations

The equation implies that the OBUs with small dwelling time, small tolerable playback delay, larger queuing delay, and larger amount of high-priority packets will be scheduled first.

EURASIP Journal on Wireless Communications and Networking

Human-verified similar examples from authoritative sources

Similar Expressions

52 human-written examples

The equation implied that the constant with a value of 85.53 (see Eq. (4)) which is independent of any factor or interaction between factors suggests that the average removal of As III) by MPKSF was 85.53%.

Applied Water Science

The nature of this equation implies that boundary conditions must be applied to solve it.

Advanced Structural and Chemical Imaging

According to Parseval's theorem, the energy in a signal S t) is given as follows [ 16, 17]: (6) ∫ S (t ) 2 d t = ∑ l = − ∞ ∞ c (l ) 2 + ∑ j = 0 ∞   ∑ k = − ∞ ∞ d j (k ) 2. This equation implies that the energy of a signal is the summation of low-frequency and high-frequency coefficients.

BioMed Research International

} end{aligned}which is the same since the first equation implies that the extra term in the second vanishes.

Bulletin of Mathematical Sciences

The first equation implies that the difference between the mapped distances of matepair X i and X j are preserved.

Bioinformatics

Expert writing Tips

Best practice

For formal writing, follow with a clear explanation of how the equation leads to the stated implication.

Common error

Avoid using "the equation implies that" when the connection between the equation and the conclusion is weak or requires additional assumptions. Instead, use weaker terms like "suggests" or "indicates".

Linguistic Context

The phrase "the equation implies that" serves as a connector to introduce a logical consequence or conclusion that directly results from a given equation. This is supported by Ludwig, which classifies it as correct and usable.

Expression frequency: Uncommon

Frequent in

Science

80%

Academia

10%

Formal & Business

5%

Less common in

News & Media

2%

Encyclopedias

1%

Wiki

2%

Ludwig's WRAP-UP

In summary, "the equation implies that" is a grammatically correct and usable phrase, as confirmed by Ludwig, primarily used in formal scientific and academic contexts to present direct logical consequences of mathematical equations. While it's not extremely common, it serves an important function in presenting deductions, and should be used when there is a clear, direct link between the equation and the conclusion. Alternatives like "the equation suggests that" or "the equation indicates that" may be more appropriate when the connection is less definitive. When using this phrase, always ensure the implication is clear and well-supported.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

the equation suggests that

Replaces "implies" with "suggests", indicating a less definitive conclusion.

the equation indicates that

Uses "indicates" instead of "implies", suggesting a pointing-to relationship rather than a direct consequence.

the equation demonstrates that

Emphasizes the equation's power to showcase or prove something.

from the equation, it follows that

Changes the structure to highlight the deduction process.

this equation leads to the conclusion that

Focuses on the equation as the starting point of a logical progression.

as a result of the equation

Highlights the result or outcome derived from the equation.

consequently, the equation shows that

Introduces the result as a consequence shown by the equation.

therefore, the equation reveals that

Signifies the revelation or discovery resulting from the equation.

the consequence of the equation is that

Highlights the outcome of the equation.

it can be inferred from the equation that

Stresses the act of drawing a conclusion from the equation.

FAQs

What does "the equation implies that" mean?

The phrase "the equation implies that" means that a particular equation logically leads to a specific conclusion or outcome. It suggests a direct relationship where the equation's properties necessitate the stated result.

What are some alternatives to "the equation implies that"?

Alternatives include "the equation suggests that", "the equation indicates that", or "from the equation, it follows that". The best choice depends on the strength of the logical connection you want to convey. See also "the equation suggests that".

Is it appropriate to use "the equation implies that" in formal writing?

Yes, "the equation implies that" is appropriate for formal and scientific writing, especially when presenting mathematical or logical deductions. Ensure the implication is clear and well-supported.

What's the difference between "the equation implies that" and "the equation suggests that"?

"The equation implies that" indicates a stronger, more direct logical consequence. "The equation suggests that" indicates a weaker connection, where the equation hints at a possibility but does not guarantee it. Use "the equation suggests that" when the relationship is less definitive.