approximate equality

USAGE SUMMARY

The phrase "approximate equality" is correct and usable in written English.
It can be used in mathematical or scientific contexts to describe a situation where two values are close in value but not exactly the same. Example: "In this experiment, we found that the two measurements showed approximate equality, indicating that our results were consistent."

✓ Grammatically correct

Science

Encyclopedias

News & Media

Human-verified examples from authoritative sources

Exact Expressions

29 human-written examples

It is reasonable to replace (1) by an approximate equality as follows: (3).

EURASIP Journal on Wireless Communications and Networking

where ≈ ρ → ∞ means approximate equality when ρ tends to be infinite.

EURASIP Journal on Wireless Communications and Networking

The majority of values appear to be concentrated around zero, indicating approximate equality.

Mathematics-in-Industry Case Studies

Also, by observing these figures, we can yield the approximate equality of the PA and TS methods.

Journal of Industrial Engineering International

Moreover, the validity of the approximate equality in Eq. (7) will be examined in Section 2 of the Additional file 1.

Earth, Planets and Space

Dramatically, when data size is largeref:adam.1996 marg the methods give approximate equality Fig. 3 Number of coalitions vs (gamma) Fig. 4 Number of coalitions vs (beta).

Human-centric Computing and Information Sciences

Human-verified similar examples from authoritative sources

Similar Expressions

30 human-written examples

Then, after adding an appropriate error term, all of the above approximate equalities can be rephrased as inequalities.

Wikipedia

In the formulas above we used approximate equalities to reflect the fact that on the right-hand side are the data-based estimates of these quantities.

BMC Genomics

Our curriculums, in history and other subjects, must present young people with a balanced appreciation of the roles of men and women if their notions of 'man' and 'woman' are to reflect anything approximating equality.

The Guardian

Error rates were arcsin √p transformed to achieve approximate variance equality [ 27].

Behavioral and Brain Functions

Rates of correct responses were arcsin√p transformed to achieve approximate variance equality [ 33].

Behavioral and Brain Functions

Expert writing Tips

Best practice

When using "approximate equality" in mathematical or scientific writing, specify the degree of approximation or the error bounds to provide context.

Common error

Avoid using "approximate equality" when the values are significantly different. Ensure that the level of approximation is reasonable and justifiable within the context.

Linguistic Context

The phrase "approximate equality" functions as a noun phrase, often acting as a subject or object in a sentence. As Ludwig AI confirms, it's used to describe a relationship where two values or quantities are nearly, but not perfectly, equal. Examples in Ludwig show its use in scientific and mathematical contexts.

Expression frequency: Common

Frequent in

Science

80%

Encyclopedias

10%

News & Media

10%

Less common in

Formal & Business

0%

Wiki

0%

Social Media

0%

Ludwig's WRAP-UP

In summary, "approximate equality" is a noun phrase used to denote a near equivalence between two values or quantities. Ludwig AI states that it is correct and suitable for use in written English, particularly in scientific and mathematical fields. While "equality" implies an exact match, "approximate equality" acknowledges that some degree of difference exists but is often insignificant in the given context. Alternative phrases such as "near equality" or "close approximation" can be used depending on the specific nuances you wish to convey. When using this term, it is crucial to specify the degree of approximation or error bounds to ensure clarity and avoid overstating the closeness of the values.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

approximate equivalence

Replaces "equality" with "equivalence", keeping the meaning of being close but not exactly the same.

near equality

Focuses on the closeness of the values being compared.

almost equal

A more direct and less formal way of saying "approximate equality".

close approximation

Highlights that the equality is not exact but a good estimate.

rough equivalence

Emphasizes that the equality is not precise but sufficient for the purpose.

practical equivalence

Suggests that the difference is negligible for practical applications.

substantially equal

Highlights that the values are largely the same, with minor discrepancies.

essential sameness

Focuses on the shared characteristics despite minor differences.

virtual equality

Indicates that the difference is so small as to be almost nonexistent.

comparable magnitude

Shifts the focus to the size or extent of the quantities being compared.

FAQs

How can I use "approximate equality" in a sentence?

You can use "approximate equality" to indicate that two values are nearly the same but not exactly equal, such as, "The experiment showed an "approximate equality" between the predicted and observed results".

What's a good alternative to "approximate equality"?

Depending on the context, you could use phrases like "near equality", "close approximation", or "rough equivalence".

In what situations is it appropriate to use the term "approximate equality"?

The term "approximate equality" is appropriate when dealing with empirical measurements, numerical computations, or models where exact equality is unlikely or impossible to achieve.

Is there a mathematical symbol for "approximate equality"?

Yes, the symbol ≈ or ≈ can be used to denote "approximate equality". For instance, you might write a ≈ b to indicate that a is approximately equal to b.