this completes the proof

USAGE SUMMARY

"this completes the proof" is correct and can be used in written English.
You can use it when you have finished proving something, to indicate that the proof is now complete. For example, "We have shown that the equation holds for all natural numbers; this completes the proof."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

This completes the proof of the theorem.

SEP

This completes the proof. square ). square

SERIEs

This completes the proof as.

Journal of Inequalities and Applications

Then this completes the proof.

Journal of Inequalities and Applications

This completes the proof for.

Journal of Inequalities and Applications

Therefore, this completes the proof.

Journal of Inequalities and Applications

Thus this completes the proof.

Journal of Inequalities and Applications

Hence this completes the proof.

Journal of Inequalities and Applications

And this completes the proof.

Complex Adaptive Systems Modeling

This completes the proof. square )  . square

SERIEs

So this completes the proof.

Advances in Difference Equations

Expert writing Tips

Best practice

Use "this completes the proof" to signal the end of a mathematical or logical argument, ensuring clarity for the reader by explicitly stating the conclusion of your reasoning.

Common error

Avoid using redundant phrases such as "this completes the proof, thus..." as the "this completes the proof" already indicates the concluding nature of the statement. Adding 'thus' or similar words can make the writing sound repetitive.

Linguistic Context

The phrase "this completes the proof" functions as a declarative statement used to explicitly signal the conclusion of a logical or mathematical argument. As Ludwig AI confirms, the phrase is grammatically correct and serves to inform the reader that the preceding steps have successfully established the stated claim.

Expression frequency: Very common

Frequent in

Science

95%

Academia

3%

Formal & Business

1%

Less common in

News & Media

0.5%

Encyclopedias

0.3%

Wiki

0.2%

Ludwig's WRAP-UP

In summary, "this completes the proof" is a grammatically sound and highly prevalent phrase predominantly used in scientific and academic writing to denote the culmination of a logical argument or mathematical proof. According to Ludwig AI, the phrase is indeed correct and suitable for use. While alternatives exist, such as "this concludes the demonstration" or "this validates the theorem", the original phrase remains a clear and concise method for indicating that a proof has reached its successful conclusion. It's essential to avoid redundancy by not adding unnecessary transitional phrases after "this completes the proof". The phrase's primary purpose is to signal finality and validation, making it an essential element in formal, rigorous writing.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

this concludes the demonstration

Replaces "proof" with "demonstration", implying a more visual or practical validation rather than a purely logical one.

this marks the end of the proof

Emphasizes the termination point of the proof process, focusing on the sequential nature of the argument.

this validates the theorem

Shifts the focus to the validation of a theorem rather than the completion of the proof process.

this establishes the result

Highlights the establishment of a specific result or finding as the culmination of the proof.

this verifies the claim

Emphasizes the verification of a specific claim or statement made at the beginning of the argument.

the proof is now complete

Changes the sentence structure to a passive voice, emphasizing the state of the proof rather than the action of completing it.

hence, the proof is finished

Adds a causal connector "hence" to explicitly link the preceding steps to the completion of the proof.

therefore, the proof is done

Uses "done" instead of "complete" or "finished", providing a more informal alternative.

this serves as proof

Indicates that the preceding argument fulfills the requirements to be considered a valid proof.

this definitively proves

Adds the adverb "definitively" to highlight the conclusive nature of the proof.

FAQs

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

"This completes the proof" is typically used at the end of a mathematical or logical argument to clearly indicate that the proof has been successfully concluded. For example, "After demonstrating all necessary steps, "this completes the proof"."

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

Alternatives include "this concludes the demonstration", "this validates the theorem", or "the proof is now complete". The choice depends on the context and the specific nuance you wish to convey.

Is it appropriate to use "this completes the proof" in formal writing?

Yes, "this completes the proof" is perfectly appropriate for formal writing, particularly in academic and scientific contexts where proofs are common. It provides a clear and concise way to signal the conclusion of a logical argument.

Can I use "this completes the proof" in non-mathematical contexts?

While primarily used in mathematical or logical contexts, "this completes the proof" can be adapted to other situations where you're presenting a well-reasoned argument or demonstration. However, ensure that the context genuinely involves a logical progression and conclusion akin to a formal proof. Using other alternatives may provide a better reading experience in non-mathematical context.