for all pairs

USAGE SUMMARY

The phrase "for all pairs" is correct and usable in written English.
It is typically used in mathematical or logical contexts to indicate that a statement or condition applies to every possible pair of elements in a given set. Example: "The theorem holds true for all pairs of integers."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

For all pairs and such that, (28).

EURASIP Journal on Information Security

Repeat step 2 for all pairs (j,m).  .

EURASIP Journal on Advances in Signal Processing

for all pairs in, where is a positive constant and.

Boundary Value Problems

holds for all pairs of real numbers u ≠ 0 and v.

Journal of Inequalities and Applications

The above conditions define universal peering constraints for all pairs of agents.

Complex Adaptive Systems Modeling

A fixed initial curve can be used for all pairs of images.

EURASIP Journal on Image and Video Processing

Note that the above optimization maximizes the minimum Euclidean distance for all pairs of transmitters.

EURASIP Journal on Wireless Communications and Networking

These assumptions make the calculation of possible for all pairs of terminal nodes and questions.

EURASIP Journal on Advances in Signal Processing

To test, we compared the 90th percentile values by mapping region for all pairs of maps.

Carbon Balance and Management

Hence, | β j i | ≤ | β i i | holds for all pairs i, j.

Journal of Inequalities and Applications

The optimal modulation amount ζ ab is calculated for all pairs.

EURASIP Journal on Advances in Signal Processing

Expert writing Tips

Best practice

When using "for all pairs", ensure the context clearly defines what constitutes a 'pair'. Ambiguity can lead to misinterpretation, especially in technical writing. For example, specify if order matters in the pairing.

Common error

Avoid assuming the reader understands the criteria for forming pairs. Explicitly state whether the pairs are ordered or unordered, and if elements can be paired with themselves (e.g., (a, a)).

Linguistic Context

The phrase "for all pairs" functions as a prepositional phrase introducing a universal quantifier. It specifies that a particular action, condition, or property applies to every possible combination of two elements within a defined set. Ludwig AI confirms its grammatical correctness and usability.

Expression frequency: Very common

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Academia

0%

Ludwig's WRAP-UP

In summary, the phrase "for all pairs" is a grammatically sound and very common construct, predominantly used in formal and scientific contexts. As Ludwig AI confirms, it signifies that a certain condition applies universally to every possible dyad within a specified set. When employing this phrase, clarify the criteria defining a 'pair' to avoid ambiguity. Alternatives like "for each pair" or "for every pair" offer similar meanings. The high source quality and consistent usage patterns indicate its reliability in technical writing.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

for each pair

This alternative is a more direct and less formal way of saying "for all pairs".

for every pair

This alternative is very similar in meaning and formality to "for each pair", offering a slightly different emphasis.

for any two

This alternative emphasizes the selection of two items from a set, implying that the statement holds regardless of which two are chosen.

for each couple

This alternative is suitable when specifically referring to pairs that are naturally or intentionally grouped together.

pairwise for all

This alternative reorders the words to emphasize the pairwise nature of the operation or comparison being performed.

for every combination of two

This alternative is more explicit about the combinatorial aspect of selecting pairs.

in all paired instances

This alternative is more formal and emphasizes the existence of paired instances.

considering all duos

This alternative uses the word 'duos,' which is less formal and may be suitable for less technical contexts.

with all pairings

This alternative focuses on the act of pairing and the implications thereof.

across all couples

This alternative is more conversational while retaining the concept of considering every pair.

FAQs

How to use "for all pairs" in a sentence?

Use "for all pairs" to indicate that a certain condition or operation applies to every possible combination of two elements from a set. For example: "The distance was calculated for all pairs of points in the dataset."

What can I say instead of "for all pairs"?

You can use alternatives like "for each pair", "for every pair", or "for any two" depending on the context.

Is it necessary to define the set when using "for all pairs"?

Yes, clearly defining the set from which the pairs are drawn is crucial. For example, state "for all pairs of numbers in the set S" to avoid ambiguity.

Does "for all pairs" imply ordered or unordered pairs?

The phrase itself does not specify order. If order matters, clarify by saying "for all ordered pairs". Otherwise, it's generally assumed the order does not matter (i.e., (a, b) is the same as (b, a)).