an even integer

USAGE SUMMARY

The phrase "an even integer" is correct and usable in written English.
It can be used in mathematical contexts to refer to any whole number that is divisible by 2 without a remainder. Example: "In this equation, we need to find an even integer that satisfies the given conditions."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

57 human-written examples

with an even integer.

EURASIP Journal on Advances in Signal Processing

Fix an even integer k.

Advances in Difference Equations

Also let s be an even integer.

Advances in Difference Equations

Let be an even integer number, with and vector spaces.

Journal of Inequalities and Applications

If is an even integer, then we have.

Journal of Inequalities and Applications

Komori and Mizuhara [7] removed the restriction '(n-alpha) is an even integer'.

Journal of Inequalities and Applications

Theorem 3.5 Let p > 1 and p ≠ n where p is not an even integer.

Journal of Inequalities and Applications

Let, an even integer, an Abelian group, and a complete normed Abelian group.

Journal of Inequalities and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

3 human-written examples

More precisely, as Carlitz has pointed out [[17], p.184], if y is a fixed even integer ≥2 and f n ( x ) is an arbitrary normalized polynomial of degree n, then (29) determines g n − 1 ( x ) as a normalized polynomial of degree n − 1.

Fixed Point Theory and Applications

Lemma 11 (a) Suppose 1 < c < 10 1 / 4. Then there exist a rational ε = ε ( c ) > 0 and a positive even integer k = k ( c ) such that the pair ( k, ε ) is c-friendly under subtle coding.

Advances in Difference Equations

Lemma 10 Suppose 1 < c < 3. Then there exist a rational ε = ε ( c ) > 0 and a positive even integer k = k ( c ) such that the pair ( k, ε ) is c-friendly under robust coding.

Advances in Difference Equations

Expert writing Tips

Best practice

In programming contexts, verify that your code correctly identifies and processes "an even integer" when such a condition is required. Use the modulo operator (%) to check for divisibility by 2.

Common error

Avoid using "an even integer" when simply referring to any even number. While all even integers are even numbers, not all contexts require the formal specification of the number being an integer. Use "even number" in more general contexts.

Linguistic Context

The phrase "an even integer" functions as a modifier specifying a particular type of number that is both an integer (a whole number) and even (divisible by 2). Ludwig AI indicates the phrase is grammatically correct and commonly used in technical contexts.

Expression frequency: Very common

Frequent in

Science

99%

News & Media

0.5%

Formal & Business

0.5%

Less common in

Wiki

0%

Encyclopedias

0%

Reference

0%

Ludwig's WRAP-UP

In summary, the phrase "an even integer" is a grammatically sound and frequently used term, predominantly found in scientific and mathematical texts. It serves the function of precisely defining a number as a whole number divisible by 2. Given Ludwig AI's validation and the phrase's prevalence in formal contexts, writers can confidently employ "an even integer" when clarity and mathematical accuracy are required. Remember to favor "even number" for general usage and ensure that the mathematical and programming conditions where you must utilize it are well defined.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

even number

This is a more concise and common term for the same concept.

multiple of two

This alternative highlights the divisibility aspect of an even integer.

integer divisible by two

This explicitly states the defining characteristic of an even integer.

whole number divisible by two

This is slightly more verbose but emphasizes that even integers are whole numbers.

even whole number

Similar to "whole number divisible by two", it emphasizes the 'whole number' property.

integer in the form of 2n

This expresses even integers using algebraic notation.

number exactly divisible by 2

This alternative specifies that the division leaves no remainder.

positive even integer

This restricts the set to only positive numbers, excluding zero and negative even integers.

non-negative even integer

This includes zero and positive even integers.

an element of the set of even numbers

This defines it in terms of set membership.

FAQs

How can I use "an even integer" in a sentence?

You can use "an even integer" to specify a number divisible by 2 in mathematical or programming contexts. For example: "The algorithm requires "an even integer" as input."

What is the difference between "an even integer" and "an even number"?

"An even integer" specifically refers to a whole number divisible by 2. "An even number" can include non-integers such as 2.5 * 2 = 5, which may not always be appropriate depending on the context. Therefore, using ""an even integer"" is more precise when needing a whole number.

What are some synonyms for "an even integer"?

Synonyms include "even number", "multiple of two", and "integer divisible by two", although the best choice depends on the specific context and desired level of formality.

Why is it important to specify "an even integer" in certain contexts?

Specifying "an even integer" is crucial in mathematical proofs, computer algorithms, and other formal settings where the properties of whole numbers divisible by 2 are essential. It ensures clarity and avoids potential errors from using non-integer even numbers.