a rigorous proof of

USAGE SUMMARY

The phrase "a rigorous proof of" is correct and usable in written English.
It can be used in contexts where you are discussing the validity or correctness of a statement, theorem, or mathematical concept. Example: "The mathematician presented a rigorous proof of the theorem, leaving no room for doubt."

✓ Grammatically correct

Science

Encyclopedias

News & Media

Human-verified examples from authoritative sources

Exact Expressions

30 human-written examples

An early use of the new methods was a rigorous proof of the ergodic theorem by American mathematician George David Birkhoff in 1931.

Encyclopedia Britannica

Even so, a rigorous proof of correctness is rarely forthcoming.

SEP

In this paper, we will give a rigorous proof of some arguments of Ishimura.

Journal of Functional Analysis

Unfortunately, there is no a rigorous proof of convergence to date.

IFAC Proceedings Volumes

Second, we give a rigorous proof of the propagation of the chaos property.

The Journal of Mathematical Neuroscience

However, a rigorous proof of the convergence and optimality of the proposed algorithm is not provided.

EURASIP Journal on Wireless Communications and Networking

Human-verified similar examples from authoritative sources

Similar Expressions

29 human-written examples

In this section, we will give a rigorous proof for security of SAM under the CK model.

EURASIP Journal on Wireless Communications and Networking

Further, we provide a rigorous proof for the tightness of SDP relaxation in worst SINR maximization problem in multi-cell downlink scenario with a single user per cell and subject to interference temperature constraints.

EURASIP Journal on Wireless Communications and Networking

In the past year Schwinger's conjecture was given a rigorous proof by Charles Fefferman of Princeton University and L.A. Seco of the University of Toronto.

Encyclopedia Britannica

Deduction, in logic, a rigorous proof, or derivation, of one statement (the conclusion) from one or more statements (the premises)—i.e., a chain of statements, each of which is either a premise or a consequence of a statement occurring earlier in the proof.

Encyclopedia Britannica

One can ask for a rigorous proof (or disproof) of it.

Journal of Inequalities and Applications

Expert writing Tips

Best practice

When using "a rigorous proof of", ensure that the supporting evidence and logical steps are clearly articulated and can withstand scrutiny. Provide sufficient detail to allow readers to independently verify the conclusion.

Common error

Avoid claiming "a rigorous proof of" if the evidence is preliminary or based on assumptions that have not been fully validated. Using less assertive language may be more appropriate in such cases.

Linguistic Context

The phrase "a rigorous proof of" functions as a noun phrase that identifies something—typically a theorem, concept, or argument—that has been demonstrated to be true through a logically sound and thoroughly justified process. As noted by Ludwig AI, this phrase suggests the presence of definitive and verifiable evidence.

Expression frequency: Common

Frequent in

Science

70%

Encyclopedias

15%

News & Media

10%

Less common in

Formal & Business

2%

Wiki

2%

Reference

1%

Ludwig's WRAP-UP

In summary, "a rigorous proof of" is a phrase used to assert that something is definitively proven through a logical and well-justified process. Ludwig AI confirms the phrase is grammatically correct and commonly encountered in academic and scientific writing. Its primary contexts include science, encyclopedias, and news media, with a formal and scientific register. When using the phrase, it's crucial to ensure the proof is indeed rigorous and that supporting evidence is clearly presented. Alternatives such as "a strict verification of" or "a compelling demonstration of" may be suitable depending on the intended emphasis. The key is to accurately reflect the level of certainty and evidence supporting the claim.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

a strict verification of

Emphasizes the exactness and adherence to rules in the verification process.

a thorough validation of

Focuses on the completeness and depth of the validation process.

a solid justification for

Highlights the provision of strong and defensible reasons.

a compelling demonstration of

Stresses the convincing and persuasive nature of the demonstration.

a definitive confirmation of

Indicates a final and conclusive establishment of truth.

an irrefutable argument for

Suggests a claim that cannot be disproven through reasoning.

a watertight case for

Emphasizes the impenetrability and strength of the presented argument.

an exact substantiation of

Focuses on providing precise evidence or support.

a detailed exposition of

Highlights the extensive explanation and analysis provided.

a careful corroboration of

Stresses the cautious and confirming nature of the evidence.

FAQs

How can I use "a rigorous proof of" in a sentence?

Use "a rigorous proof of" when you want to emphasize that something has been definitively proven using sound logic and evidence. For example, "The theorem provides "a rigorous proof of" the initial hypothesis".

What are some alternatives to "a rigorous proof of"?

You can use alternatives like "a strict verification of", "a thorough validation of", or "a compelling demonstration of" depending on the context.

What does it mean for a proof to be considered "rigorous"?

A "rigorous" proof means that all steps in the proof are logically sound, well-justified, and leave no room for ambiguity or doubt. It adheres to the highest standards of mathematical or logical reasoning.

In what fields is "a rigorous proof of" most commonly used?

"A rigorous proof of" is frequently encountered in fields such as mathematics, physics, computer science, and other areas where formal logic and deductive reasoning are central.