a theorem stating that

USAGE SUMMARY

The phrase "a theorem stating that" is correct and usable in written English.
It can be used when introducing a theorem and specifying what it asserts or concludes. Example: "The Pythagorean theorem is a theorem stating that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

4 human-written examples

Finally, we state a theorem stating that the unique solution of a symmetric BVP is symmetric.

Boundary Value Problems

This result is obtained as a consequence of a theorem stating that each orthogonal form on a C*-algebra is determined by two functionals on the algebra.

Journal of Functional Analysis

Under reasonable assumptions on this map, Breuer is able to prove a theorem stating that no such map can exist that can distinguish all the states of the system.

SEP

For example, a theorem stating that the angle of a triangle is a right angle would not be a false statement since there are indeed triangles with right angles.

SEP

Human-verified similar examples from authoritative sources

Similar Expressions

56 human-written examples

As applications, we will prove a density theorem stating that smooth functions with compact support are dense in Bm,p(G) modulus a finite-dimensional subspace.

Journal of Functional Analysis

There is a general theorem stating that the system of equations F x) = g, where x ∈ R n, F is a differentiable function F : R n → R n, and F x0) = g0, can only have a differentiable solution x = G(g), x0 = G g0), if there is a feedback loop involving all n variables [ 27, 47].

BMC Systems Biology

They proved two important theorems: a local-global theorem stating that if a finite-dimensional central division algebra over a number field splits locally everywhere then it splits globally (so is trivial), and from this, deduced their Hauptsatz ("main theorem"): every finite dimensional central division algebra over an algebraic number field F splits over a cyclic cyclotomic extension.

Wikipedia

In particular in Section 3, we prove an analogue of the theorem stating that a compact convex set in R N is the convex hull of its extremal points.

Journal of Inequalities and Applications

In Sect. 3 the notion of a contractive IFS F = { X ; f 1, f 2,, f N } is defined, followed by Hutchinson's theorem stating that a contractive IFS has a unique attractor.

Bulletin of Mathematical Sciences

This should be contrasted with Tarski's theorem stating that the unrestricted T-schema is inconsistent.

SEP

Fermat's theorem, stating that Ax + Bx = Cx has no solution in positive integers for x>2, was famously proved 357 years after Pierre de Fermat proposed it.

Forbes

Expert writing Tips

Best practice

When introducing a theorem, follow "a theorem stating that" with a clear and concise statement of the theorem's conclusion or assertion. Ensure the statement is grammatically correct and accurately reflects the theorem's meaning.

Common error

Avoid using "a theorem stating that" followed by a vague or oversimplified description. Provide a complete and accurate summary of the theorem's core assertion to prevent misunderstanding.

Linguistic Context

The phrase "a theorem stating that" functions as an introductory phrase to present or define a mathematical or logical theorem. It sets up the expectation that a precise statement or assertion will follow. As Ludwig AI points out, it is a grammatically correct phrase.

Expression frequency: Uncommon

Frequent in

Science

75%

Encyclopedias

8%

Wiki

8%

Less common in

News & Media

8%

Formal & Business

0%

Social Media

0%

Ludwig's WRAP-UP

In summary, "a theorem stating that" is a grammatically sound phrase used to introduce a formal theorem and articulate its core assertion. Ludwig AI confirms its correctness and usability. This phrase is most frequently found in scientific and academic contexts. While variations exist, such as "a theorem asserting that" or "a theorem which claims that", the core function remains the same: to precisely and clearly convey the essence of the theorem being presented. When using this phrase, avoid vagueness and ensure the following statement accurately reflects the theorem's meaning.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

a theorem asserting that

Replaces "stating" with "asserting", focusing on the act of declaring or claiming something is true.

a theorem which claims that

Uses "which claims" instead of "stating", emphasizing the theorem's claim or proposition.

a theorem postulating that

Substitutes "stating" with "postulating", suggesting the theorem introduces a fundamental condition or hypothesis.

a theorem indicating that

Replaces "stating" with "indicating", highlighting the theorem's role in pointing out or suggesting something.

a theorem showing that

Uses "showing" instead of "stating", focusing on the theorem's demonstration or proof.

a theorem establishing that

Substitutes "stating" with "establishing", emphasizing the theorem's role in confirming or proving something.

a theorem from which it follows that

Rephrases the entire structure to focus on the logical consequence of the theorem.

the theorem stipulates that

Changes from 'a theorem stating' to 'the theorem stipulates,' placing emphasis on the theorem's prescription.

the theorem provides that

Similar to 'stipulates,' but using 'provides' to indicate the theorem supplies a specific condition or outcome.

the content of the theorem is that

Restructures the sentence to explicitly state that the following part is the content of the theorem.

FAQs

How can I use "a theorem stating that" in a sentence?

Use "a theorem stating that" to introduce a formal declaration or finding within a specific field. For example: "The central limit theorem is a theorem stating that the distribution of sample means approximates a normal distribution as the sample size increases."

What are some alternatives to "a theorem stating that"?

You can use alternatives like "a theorem asserting that", "a theorem which claims that", or "a theorem postulating that", depending on the nuance you want to convey.

Is it better to use "a theorem stating that" or "the theorem states that"?

The choice depends on the context. "A theorem stating that" is suitable when introducing a theorem generally. "The theorem states that" is appropriate when referring to a specific, previously mentioned theorem.

What's the difference between "a theorem stating that" and "a theorem that proves"?

"A theorem stating that" introduces the theorem's assertion, while "a theorem that proves" focuses on the theorem's function of providing proof. For instance, "Fermat's Last Theorem is a theorem stating that no three positive integers a, b, and c satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2" versus "This theorem proves the existence of a unique solution."