for some odd integer

USAGE SUMMARY

The phrase "for some odd integer" is correct and usable in written English.
It can be used in mathematical contexts when referring to an unspecified odd integer in a general statement or equation. Example: "Let x be a variable that can take on any value for some odd integer."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

18 human-written examples

If d n = 0 for some odd integer n, then g has a fixed point.

Fixed Point Theory and Applications

If is even, then for some odd integer and is odd.

Advances in Difference Equations

If is odd, then is even and for some odd integer.

Advances in Difference Equations

Since for some odd integer and is odd, by (5.32), we have (5.33).

Advances in Difference Equations

So we must have that is even and Note that and implies for some odd integer The proof is complete.

Advances in Difference Equations

Secondly, let where Recall (6.15), we see that for all By our assumption, it is easy to check that is even and for some odd integer.

Advances in Difference Equations

Human-verified similar examples from authoritative sources

Similar Expressions

42 human-written examples

Using this pair of designs, we prove there is a cocyclic Hadamard matrix of order 2ts for any odd integer s>1 and any t⩾⌊8 log2 s⌋.

Journal of Combinatorial Theory, Series A

For arbitrary odd integer (qge3), he [3] soon obtained r(1,q =frac{phi q)}{2}+O bigl(q^{1/2}d^{2}(q) ln^{2}q bigr), where (d q)) is the classical divisor function.

Journal of Inequalities and Applications

For an odd integer k≥1 and prime power q, Lazebnik et al. present explicit construction for q-regular bipartite graphs with girth at least k+5 and number of edges q k−1 [15].

EURASIP Journal on Advances in Signal Processing

Since t e t - 1 - 1 + t 2 is an even function (i.e., invariant under x ↦ - x), we see that B k = 0 for any odd integer k not smaller than 3.

Advances in Difference Equations

In detail, and it is easy to show that for an odd integer n, Since T n, 0 ( z ) = T n ( z ), we may apply results about T n, ϵ ( z ) to those about T n ( z ).

Journal of Inequalities and Applications

Expert writing Tips

Best practice

When using "for some odd integer", ensure the context clearly defines the variable or condition the integer is related to. This helps avoid ambiguity in mathematical or logical statements.

Common error

Avoid using "for some odd integer" when you need to specify that all odd integers must satisfy a condition. "Some" implies that the condition might not hold for every odd integer.

Linguistic Context

The phrase "for some odd integer" functions as an existential quantifier in mathematical and logical contexts. It asserts the existence of at least one odd integer that satisfies a certain condition. Ludwig examples show it primarily in scientific papers.

Expression frequency: Common

Frequent in

Science

95%

Encyclopedias

3%

Wiki

2%

Less common in

News & Media

0%

Formal & Business

0%

Social Media

0%

Ludwig's WRAP-UP

The phrase "for some odd integer" is a mathematically precise expression mainly used in scientific and academic writing. As Ludwig AI confirms, it's grammatically sound and relatively common in contexts requiring rigorous arguments, such as mathematical proofs. It serves to introduce a specific condition, asserting the existence of at least one odd integer satisfying the given criteria. While alternatives like "for an odd integer" exist, the key is to ensure clarity and avoid implying universality when only existence is meant. Recognizing the nuance allows for accurate and effective communication in mathematical and scientific discussions.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

with some odd integer

Synonymous to the query but slightly less formal.

for an odd integer

Replaces "some" with "an", indicating any single, unspecified odd integer.

for a certain odd integer

Emphasizes that the odd integer is specific, though not explicitly identified.

for at least one odd integer

Indicates the existence of one or more odd integers that satisfy a given condition.

for a particular odd integer

Highlights that the odd integer is specific and under consideration.

when the integer is odd

Shifts focus to the oddness of the integer as a condition.

where k is an odd integer

Specifies that "k" represents any odd integer.

if n is an odd integer

Introduces the odd integer as a condition in a conditional statement.

given an odd integer

Used when an odd integer is provided as a starting point or condition.

with an odd integer value

Emphasizes that the value is an odd integer.

FAQs

When is it appropriate to use "for some odd integer"?

Use "for some odd integer" when you need to indicate that a statement is true for at least one odd integer, but not necessarily all of them. It's used to assert the existence of an odd integer with a specific property.

What's the difference between "for some odd integer" and "for any odd integer"?

"For some odd integer" asserts the existence of at least one odd integer that satisfies a condition. In contrast, "for any odd integer" asserts that a condition is true for all odd integers.

What are some alternatives to "for some odd integer"?

Depending on the specific context, you could use alternatives like "for a certain odd integer", "for an odd integer", or "there exists an odd integer".

How do I use "for some odd integer" in a mathematical proof?

In a mathematical proof, "for some odd integer" is used to introduce an odd integer whose existence allows you to prove a statement. For example: "Assume that equation x holds true "for some odd integer" k. Then..."