the mentioned theorem

USAGE SUMMARY

The phrase "the mentioned theorem" is correct and usable in written English.
It can be used when referring to a theorem that has been previously discussed or referenced in the text. Example: "In the previous section, we proved the mentioned theorem, which establishes the relationship between the two variables."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

8 human-written examples

We present the mentioned theorem in both contexts.

Fixed Point Theory and Applications

So, our theorem is a proper generalization of the mentioned theorem from [13].

Fixed Point Theory and Applications

The mentioned theorem is generalized in metric spaces as well as in its various generalizations.

Fixed Point Theory and Applications

To prove our main claims, we will show a unidimensional proof of the mentioned theorem.

Fixed Point Theory and Applications

Indeed, we take x = u in the statement of the mentioned theorem, we get ε ≤ ψ ( d 2 ( ( x, y ), ( u, v ) ) ) = 1 2 | y − v | < ε + δ.

Journal of Inequalities and Applications

However, Theorem 3.4 provides a method to construct the dual wavelet of a given pre-wavelet without using the mentioned theorem or MRA.

Journal of Inequalities and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

52 human-written examples

We consider the following system, and the proof of the theorem is similar to the above mentioned theorem and so it is left to the reader, x n + 1 = x n y n − 2 y n − 1 ( − 1 + x n y n − 2 ), y n + 1 = y n x n − 2 x n − 1 ( − 1 − y n x n − 2 ).

Advances in Difference Equations

Hence we have the (already mentioned) theorem: (Matsumura) The automorphism group of a variety Y of general type is finite.

Bulletin of Mathematical Sciences

But we cannot invoke the above mentioned theorem of Ćirić to show the existence of a fixed point for T. To prove the following common fixed point result, we use the technique in [5].

Fixed Point Theory and Applications

But we cannot invoke the above mentioned theorem of Samet to show that the mapping T has a best proximity point in A because T is not an almost contraction.

Fixed Point Theory and Applications

However, we cannot invoke the above mentioned Theorem 3.2 of Sadiq Basha to show the existence of a best proximity point because g is not an isometry.

Fixed Point Theory and Applications

Expert writing Tips

Best practice

When using "the mentioned theorem", ensure that the theorem has been clearly and unambiguously stated earlier in the text. Avoid ambiguity by providing a specific reference if necessary.

Common error

Avoid using "the mentioned theorem" if it's not immediately clear which theorem you're referring to. If there's any possibility of confusion, restate the theorem or provide a specific citation.

Linguistic Context

The phrase "the mentioned theorem" functions as a determiner phrase specifying a particular theorem that has been previously identified within the text. Ludwig AI indicates that this phrase is grammatically sound and frequently employed in academic writing to ensure cohesion and avoid repetition. For example, "Indeed, we take x = u in the statement of the mentioned theorem, we get ε ≤ ψ ( d 2 ( ( x, y ), ( u, v ) ) ) = 1 2 | y − v | < ε + δ."

Expression frequency: Uncommon

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Encyclopedias

0%

Ludwig's WRAP-UP

In summary, "the mentioned theorem" serves as a practical way to reference a previously stated theorem in writing, predominantly within academic and scientific fields. As confirmed by Ludwig AI, the phrase is grammatically correct and widely accepted. Ensure clarity by verifying the theorem has been clearly defined before using this phrase. Alternatives such as "the aforementioned theorem" and "the previously stated theorem" offer stylistic variations, while "the theorem in question" is useful to emphasize scrutiny. Overall, "the mentioned theorem" offers precision and conciseness when referring back to a theorem already presented.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

the aforementioned theorem

Uses a more formal term, "aforementioned", instead of "mentioned".

the previously stated theorem

Emphasizes that the theorem was stated earlier.

the theorem referenced above

Highlights that the reference is in the preceding text.

the theorem discussed earlier

Focuses on the discussion aspect.

the theorem in question

Implies that the theorem is being specifically examined.

the said theorem

A more legalistic or formal way of referring to the theorem.

the theorem just stated

Emphasizes the immediacy of the prior statement.

the foregoing theorem

A more archaic and formal synonym for "aforementioned".

the specified theorem

Highlights that the theorem has specific conditions or details.

the relevant theorem

Emphasizes the importance of the theorem to the current context.

FAQs

How do I use "the mentioned theorem" in a sentence?

Use "the mentioned theorem" to refer back to a theorem that you've already introduced or discussed in your text. For example, "Applying "the mentioned theorem", we can derive the following result."

What's a formal alternative to "the mentioned theorem"?

A more formal alternative would be "the aforementioned theorem" or "the foregoing theorem".

When should I restate the theorem instead of using "the mentioned theorem"?

If the theorem was stated several paragraphs or pages earlier, or if there's a chance the reader might have forgotten the exact statement, it's better to restate it or provide a specific page or section reference instead of relying on "the mentioned theorem".

Is it okay to use "the mentioned theorem" in informal writing?

While grammatically correct, "the mentioned theorem" is more common in academic and technical writing. In informal contexts, you might rephrase it more simply, such as "the theorem I just talked about".