for every j

USAGE SUMMARY

The phrase "for every j" is correct and usable in written English.
It is typically used in mathematical or programming contexts to indicate that a statement applies to each instance of the variable j. Example: "For every j in the set, we will calculate the corresponding value of the function."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

A set D ⊆ L 2 ( I, X ) is said to be 'decomposable', if for every g 1, g 2 ∈ D and for every J ⊆ I measurable, we have χ J g 1 + χ J c g 2 ∈ D. The following lemmas are still needed in the proof of our main theorems.

Advances in Difference Equations

A set D ⊆ L 2 ( I, X ) is said to be 'decomposable', if for every g 1, g 2 ∈ D and for every J ⊆ I measurable we have χ J g 1 + χ J c g 2 ∈ D. Let X be a Banach space and let L 2 ( I, X ) be the Banach space of all functions u : I → X, which are Bochner integrable.

Journal of Inequalities and Applications

for every j ∈ ℕ.

Advances in Difference Equations

This implies that p ∈ E P ( F j ) for every j ∈ Δ.

Journal of Inequalities and Applications

Step 3 Initialize k j  = 1, for every j = 1,…, N Obj.

International Journal of Disaster Risk Science

It suffices to claim that Ψ ⊂ C n, j for every j ∈ Δ.

Fixed Point Theory and Applications

③ For every j, connect vertices v jk+i in all groups from V 1 to V k into a line.

Journal of Cloud Computing

Let F j be a bifunction from C × C to ℝ satisfying (A1 - A4) for every j ∈ Δ.

Journal of Inequalities and Applications

This implies that ({I_j,p_j{mathbb {Z}}_n}cap Dne varnothing), for every j, (1le jle s).

Mathematical Sciences

For every j fixed, by Lemma 2.1 in [8], we have ({alpha _{j}}(lambda) to0) as (lambda toinfty).

Boundary Value Problems

④ For every j, connect vertices v jk+k and v [(j+1)%k]·k+1 with an edge.  .

Journal of Cloud Computing

Expert writing Tips

Best practice

When using "for every j" in mathematical proofs or algorithms, clearly define the range or set to which 'j' belongs to avoid ambiguity.

Common error

Avoid mixing "for every j" with other quantifiers (like "there exists") without careful consideration. Incorrectly combining them can lead to logical fallacies. For example, ensure that the scope and order of quantifiers accurately reflect the intended mathematical or logical relationship.

Linguistic Context

The phrase "for every j" functions as a universal quantifier in mathematical, scientific, and programming contexts. Ludwig AI confirms its typical use to express that a statement applies to each element 'j' within a defined set.

Expression frequency: Very common

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Encyclopedias

0%

Ludwig's WRAP-UP

In summary, "for every j" is a prevalent phrase functioning as a universal quantifier, primarily in scientific and mathematical contexts. Ludwig AI indicates its correct and widespread usage to express a general rule or condition applying to all instances of a variable 'j'. When writing, ensure the range of 'j' is clearly defined and avoid mixing with existential quantifiers without careful consideration. Alternatives like "for each j" or "for all j" can be used, but "for every j" remains the most common and precise choice in formal writing.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

for each j

This alternative is a direct synonym, replacing "every" with "each" for a slightly different emphasis but maintaining the same meaning.

for all j

This alternative uses "all" instead of "every", implying a complete and unrestricted application to all instances of 'j'.

for any j

This alternative is very similar, but it might suggest that the statement holds true even if only one instance of 'j' is considered.

for any given j

This alternative adds emphasis on the fact that 'j' is a specific, albeit arbitrarily chosen, element.

for arbitrary j

This alternative stresses the generic nature of 'j', indicating that it represents any possible value within its domain.

for each and every j

This alternative uses more emphatic language than the original phrase.

in every instance of j

This alternative uses more words to convey the same meaning, focusing on individual occurrences of 'j'.

in all cases where j

This alternative shifts the focus to the cases or scenarios involving 'j', rather than 'j' itself.

with respect to each j

This alternative highlights that a certain operation or property is related to each 'j' individually.

considering each j

This alternative presents a clearer change of focus by directing the sentence on the act of "considering", in contrast with "for".

FAQs

How to use "for every j" in a sentence?

The phrase "for every j" is used to indicate that a statement applies universally to each element 'j' within a specified set. Example: "For every j between 1 and 10, calculate j squared."

What can I say instead of "for every j"?

You can use alternatives like "for each j", "for all j", or "for any j" depending on the specific context.

Is "for every j" the same as "for some j"?

No, "for every j" indicates a universal quantification, meaning the statement holds true for all 'j'. "For some j", on the other hand, indicates existential quantification, meaning the statement holds true for at least one 'j'.

What is the difference between "for every j" and "for a j"?

"For every j" implies the statement applies to all instances of 'j'. "For a j" (which is less common and often grammatically incorrect) would typically mean the statement applies to one specific, but unspecified, instance of 'j'. It is more appropriate to use "for a specific j".