for every k

USAGE SUMMARY

The phrase "for every k" is correct and usable in written English.
It is typically used in mathematical or logical contexts to indicate that a statement applies to all values of k within a specified set or range. Example: "For every k in the set of natural numbers, the equation holds true."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

55 human-written examples

Corollary 2 Let K ∗ = { k ∈ N : n − 1 ≤ k ≤ n } ∪ K for every K ∈ F, where F is the collection of all finite subsets of ℕ.

Journal of Inequalities and Applications

for every k ∈ N +.

Journal of Inequalities and Applications

for every k ∈ Z 1 ∞.

Advances in Difference Equations

If x is increasing then, while if x is decreasing then for every k.

Journal of Inequalities and Applications

Open problem For every k ≥ 1, we have a 2 k + 1 = − a 2 k.

Journal of Inequalities and Applications

(b) The function λ → C k (λ ≥ 1) is continuous for every k ∈ ℕ.

Journal of Inequalities and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

5 human-written examples

In a straightforward implementation, O Nk) time would be required for every k-means iteration.

Journal of Big Data

Once we have computed the importance score for every k-mer at every position t, we can visualize it in a few different ways.

Bioinformatics

For every k-mer length, the more reads that were used, the larger were the N50 and the total sum of assembly.

BMC Genomics

Consider the case in which, for every t∈R, one has that x k (t)=x k, for every k=1,…,N independent of time.

Journal of Statistical Distributions and Applications

Therefore, (27) is true for every (k=1,2,ldots ) .

Advances in Difference Equations

Expert writing Tips

Best practice

When using "for every k" in mathematical writing, clearly define the set or range that k belongs to in order to avoid ambiguity.

Common error

Avoid using "for every k" without specifying the context or range of possible values for k. This can lead to misunderstandings and invalidate your argument.

Linguistic Context

The phrase "for every k" functions as a universal quantifier, indicating that a statement applies to each element 'k' within a specified set or domain. Ludwig AI shows it's commonly used in mathematical and logical contexts.

Expression frequency: Common

Frequent in

Science

96%

News & Media

2%

Formal & Business

2%

Less common in

Academia

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

The phrase "for every k" serves as a universal quantifier, primarily used in formal scientific and mathematical contexts to indicate that a statement applies to all instances of 'k' within a defined scope. Ludwig AI confirms its grammatical correctness and prevalent use in academic writing. When using "for every k", ensure that the set or range of 'k' is clearly defined to avoid ambiguity and maintain the validity of your argument. Alternatives such as "for each k" or "for all k" can be used depending on the desired nuance. Remember that while mostly interchangeable, the best practice is using them with a very specific range/set. Authoritative sources like the Journal of Inequalities and Applications often employ this phrase in their publications.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

for each k

Replaces "every" with "each", offering a subtle change in emphasis but maintaining the same meaning.

for all k

Uses "all" instead of "every", providing a more direct and forceful sense of universality.

for any k

Employs "any" to indicate that the statement holds true regardless of the specific value of k.

for arbitrary k

Specifies that k can be any value, emphasizing the generality of the statement.

for all values of k

Expands the phrase to explicitly mention "values", reinforcing the scope of the statement.

for a given k

Highlights that the statement applies to a specific, though unspecified, value of k.

for every value that k can assume

More verbose and explicit, clarifying that the statement applies to all possible values of k.

irrespective of k

Indicates that the truth of the statement does not depend on the value of k.

regardless of k

Similar to "irrespective of k", showing that the statement holds true without considering the value of k.

no matter what k is

Emphasizes the independence of the statement from the specific value of k in a more informal way.

FAQs

How can I use "for every k" in a sentence?

You can use "for every k" to introduce a statement that applies universally within a defined scope. For example, "For every k ∈ N, the equation x + k = y holds true."

What are some alternatives to "for every k"?

Alternatives include "for each k", "for all k", or "for any k", depending on the nuance you wish to convey.

Is there a difference between "for every k" and "for all k"?

While both phrases express universal quantification, "for all k" is generally perceived as more direct and forceful than "for every k", but they are largely interchangeable.

When is it appropriate to use "for every k" in writing?

Use "for every k" in mathematical proofs, logical arguments, or technical documentation where you need to assert that a statement applies to each element within a defined set.