this complete the proof

USAGE SUMMARY

'this complete the proof' is correct and usable in written English.
It can be used whenever you are referring to a proof having been completed. For example: "After showing that the axiom held true, this completed the proof that the theorem was valid."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

8 human-written examples

This complete the proof that.

Journal of Inequalities and Applications

Thus, this complete the proof of Theorem 1.6.

Journal of Inequalities and Applications

This complete the proof of the theorem, for (mathbb {P}(Omega_{0})=1).

Advances in Difference Equations

This complete the proof that x ∈ F ( S ) ∩ ( A + B ) − 1 ( 0 ).

Fixed Point Theory and Applications

Therefore, ξ t → ξ* as t → 0. This complete the proof of (ii).

Journal of Inequalities and Applications

Coming back to the initial function u, this complete the proof of the symmetry of u.

Bulletin of Mathematical Sciences

Human-verified similar examples from authoritative sources

Similar Expressions

52 human-written examples

This completes the proof of the theorem.

SEP

(2.37) 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

This completes the proof as.

Journal of Inequalities and Applications

Expert writing Tips

Best practice

When using "this complete the proof", ensure that all preceding steps of the argument are logically sound and clearly presented before making this concluding statement.

Common error

Do not use "this complete the proof" if there are any unaddressed gaps or logical leaps in your argument. This phrase should only be used when the proof is genuinely and undeniably finished.

Linguistic Context

The phrase "this complete the proof" functions as a concluding statement in a logical argument. As Ludwig AI states, it signals that the preceding steps have successfully demonstrated the validity of a claim. Examples show its prevalent use in scientific and mathematical texts.

Expression frequency: Uncommon

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Encyclopedias

0%

Ludwig's WRAP-UP

In summary, "this complete the proof" is a phrase primarily used in formal and scientific writing to indicate the end of a conclusive argument. As confirmed by Ludwig AI, it is considered grammatically correct. The phrase signals that all preceding steps lead logically to the conclusion, primarily used within scientific contexts. While "this complete the proof" is not overly common, when precision in academic writing is a must, it serves as a clear indicator of a finished demonstration. Related phrases like "this concludes the demonstration" can offer stylistic variations.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

this concludes the demonstration

Replaces "proof" with "demonstration", implying a showing or explanation, rather than a formal proof.

this validates the theorem

Uses "validates" instead of "complete the proof", implying confirmation of a theorem's truth.

hence, the proposition is proven

More formal structure, replacing the active voice with a passive construction and using "proposition" instead of a general proof.

thus, the argument is substantiated

Emphasizes the support provided for an argument, rather than the completion of a formal proof.

this confirms the hypothesis

Focuses on confirming a proposed explanation (hypothesis) rather than a proof in a mathematical sense.

the foregoing establishes the result

A more formal and somewhat archaic way of saying that the preceding steps have led to the stated result.

therefore, the claim is verified

Highlights the verification aspect of a claim, differing slightly from a formal proof.

this settles the matter

Indicates that an issue or question has been definitively resolved, not necessarily through a formal proof.

this confirms the analysis

More general, indicating agreement with the analysis that was performed, and less related to the concept of mathematical proof.

we have thus proven

Rephrases to emphasize the action of proving, rather than stating the completion.

FAQs

What does "this complete the proof" mean in mathematical context?

In mathematics, "this complete the proof" is used to signal that the preceding steps have logically and conclusively demonstrated the truth of a statement or theorem.

What are some alternatives to saying "this complete the proof"?

You can use phrases like "this concludes the demonstration", "this validates the theorem", or "hence, the proposition is proven" to signal the end of a proof.

Is it appropriate to use "this complete the proof" in non-mathematical contexts?

While primarily used in mathematical or logical arguments, you could use "this complete the proof" in other contexts where you are presenting a step-by-step argument, to indicate the final conclusive step, but the mathematical connotations are strong.

How to ensure I use "this complete the proof" correctly?

Before using "this complete the proof", review your entire argument to ensure that all steps are logically sound and that no gaps remain. This phrase should be reserved for instances where the conclusion follows directly and undeniably from the preceding statements.