this concludes the proof

USAGE SUMMARY

'this concludes the proof' is correct and usable in written English.
You can use it when you want to emphasize that you have finished presenting evidence or a logical argument to support a claim or idea. For example, "After providing several examples, this concludes the proof that raising the speed limit on this highway will lead to an increase in accidents."

✓ Grammatically correct

Science

Academia

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

This concludes the proof that NP ⊆ PCP[O log n), O(1)]!

University of California, Berkeley

end{aligned} (43) This concludes the proof.

Advances in Difference Equations

This concludes the proof of Lemma 6. □.

Journal of Inequalities and Applications

This concludes the proof of Part (i).

Journal of Inequalities and Applications

This concludes the proof of the lemma.

EURASIP Journal on Wireless Communications and Networking

This concludes the proof of Proposition 3.4.

Journal of Inequalities and Applications

This concludes the proof of the theorem.

Complex Analysis and its Synergies

This concludes the proof of assumption 1.

EURASIP Journal on Advances in Signal Processing

end{aligned} This concludes the proof.

Journal of Inequalities and Applications

This concludes the proof of (a).

Advances in Difference Equations

This concludes the proof of this lemma.

Fixed Point Theory and Applications

Expert writing Tips

Best practice

Use "this concludes the proof" to clearly signal the end of a mathematical or logical argument, ensuring readers understand the demonstration is complete. Employ it strategically to mark closure and enhance clarity.

Common error

Avoid using "this concludes the proof" in contexts that are not related to mathematical or logical proofs. Overuse in casual writing can sound pretentious and out of place. Stick to using it within formal demonstrations or arguments.

Linguistic Context

The phrase "this concludes the proof" serves as a declarative statement that marks the end of a logical or mathematical argument. Ludwig AI confirms its grammatical correctness and common usage. It signals closure and finality to the reasoning presented.

Expression frequency: Very common

Frequent in

Science

65%

Academia

35%

Formal & Business

0%

Less common in

News & Media

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

In summary, "this concludes the proof" is a grammatically correct and frequently used phrase to formally indicate the end of a mathematical or logical argument, as confirmed by Ludwig AI. Predominantly found in scientific and academic contexts, it serves to signal closure and clarity. While effective in its intended setting, overuse in informal contexts should be avoided. Consider alternatives like "therefore, the proof is complete" or "the proof is thus established" to suit different levels of formality. Ensure its appropriate application to maintain precision and avoid pretension.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

therefore, the proof is complete

Replaces the introductory phrase with a direct statement of completion and includes the connector 'therefore'.

the proof is thus established

Replaces "concludes" with "is thus established", offering a more formal tone.

hence, we have proven

Uses "hence" as a more concise connector indicating the completion of the proof.

in summary, the proof holds

Introduces a summary aspect while affirming the validity of the proof.

this validates the proof

Emphasizes validation rather than conclusion, suitable when confirming an existing proof.

the foregoing demonstrates the proof

Uses "the foregoing" to refer back to the prior argument, implying conclusion.

as shown above, the proof is valid

Refers explicitly to prior steps and affirms validity, rather than simply concluding.

we have thus achieved the proof

Highlights the achievement of the proof, suitable for emphasizing a significant result.

the demonstration is now complete

Replaces "proof" with "demonstration" and focuses on the state of being complete.

the analysis concludes the proof

Highlights analysis as a key step in the proof

FAQs

How can I use "this concludes the proof" in a sentence?

You can use "this concludes the proof" to signal the end of a mathematical or logical argument. For example, "After demonstrating each step rigorously, this concludes the proof of the theorem."

What are some alternatives to "this concludes the proof"?

Alternatives include "therefore, the proof is complete", "the proof is thus established", or "hence, we have proven", depending on the level of formality you want to convey.

When is it appropriate to use "this concludes the proof"?

It's appropriate to use "this concludes the proof" in formal settings such as academic papers, mathematical demonstrations, and logical arguments where you are presenting a rigorous proof. Avoid using it in informal contexts.

Is "this concludes the proof" the same as "QED"?

While both signal the end of a proof, "this concludes the proof" is a more descriptive statement, whereas QED (quod erat demonstrandum) is a Latin abbreviation traditionally used in mathematical proofs. The former is more accessible to a wider audience.