Formal Proof in a sentence
(1) The student's formal proof contained a logical flaw.
(2) The formal proof confirmed the conjecture to be true.
(3) The scientist provided a formal proof for the hypothesis.
(4) The formal proof was scrutinized by experts in the field.
(5) The mathematician presented a formal proof of the theorem.
(6) The formal proof relied heavily on mathematical induction.
(7) The formal proof demonstrated the validity of the equation.
(8) The mathematician spent months working on the formal proof.
(9) The lawyer presented a formal proof to support his argument.
(10) The formal proof of the lemma was based on a counterexample.
Formal Proof sentence
(11) The formal proof demonstrated the soundness of the argument.
(12) The mathematician provided a formal proof for the conjecture.
(13) The formal proof demonstrated the validity of the hypothesis.
(14) The formal proof was presented in a clear and concise manner.
(15) The complexity of the problem required a lengthy formal proof.
(16) The formal proof was written in a rigorous and precise manner.
(17) The judge demanded a formal proof of the defendant's innocence.
(18) The formal proof of the theorem required several complex steps.
(19) The formal proof was verified by multiple experts in the field.
(20) The computer program generated a formal proof for the algorithm.
Formal Proof make sentence
(21) The formal proof of the theorem was presented at the conference.
(22) The formal proof was based on a set of axioms and logical rules.
(23) The formal proof confirmed the conjecture made by the researcher.
(24) The formal proof of the proposition was outlined in the textbook.
(25) The formal proof of the lemma was crucial in solving the problem.
(26) The student struggled to construct a formal proof for the problem.
(27) In mathematics, a formal proof is a rigorous and logical argument.
(28) The formal proof of the proposition required the use of induction.
(29) The formal proof involved a series of logical steps and deductions.
(30) The formal proof was a testament to the power of logical reasoning.
Sentence of formal proof
(31) The formal proof was published in a prestigious mathematics journal.
(32) The formal proof relied on the principles of mathematical induction.
(33) The formal proof required careful attention to detail and precision.
(34) The student's formal proof was praised for its clarity and coherence.
(35) The formal proof provided a step-by-step explanation of the solution.
(36) The formal proof of the equation was presented in the research paper.
(37) The formal proof established a solid foundation for further research.
(38) The formal proof was a breakthrough in the field of computer science.
(39) The mathematician's formal proof was met with skepticism by his peers.
(40) The formal proof required the use of advanced mathematical techniques.
Formal Proof meaningful sentence
(41) The formal proof served as the basis for further research in the area.
(42) The formal proof of the corollary was presented during the conference.
(43) The formal proof of the corollary was derived from a previous theorem.
(44) The student's formal proof was rejected due to a logical inconsistency.
(45) The formal proof of the hypothesis was published in a renowned journal.
(46) The formal proof of the theorem relied on the principles of set theory.
(47) The formal proof provided a systematic approach to solving the problem.
(48) The formal proof involved the use of mathematical symbols and notation.
(49) The formal proof was a culmination of years of study and investigation.
(50) The formal proof shed light on the underlying structure of the problem.
Formal Proof sentence examples
(51) The mathematician's formal proof was published in a prestigious journal.
(52) The jury was convinced by the formal proof presented by the prosecution.
(53) The formal proof was met with admiration and applause from the audience.
(54) The student's formal proof was commended for its elegance and simplicity.
(55) The professor emphasized the importance of a well-structured formal proof.
(56) The formal proof required a deep understanding of the underlying concepts.
(57) The mathematician's formal proof revolutionized the field of number theory.
(58) The student struggled to construct a formal proof for the complex equation.
(59) The formal proof showcased the elegance and rigor of mathematical reasoning.
(60) The formal proof served as a basis for developing new mathematical theories.
Sentence with formal proof
(61) The formal proof was a result of collaboration between multiple researchers.
(62) The formal proof of the algorithm's termination was based on loop invariants.
(63) The formal proof provided a solution to a long-standing mathematical problem.
(64) The provability of the theorem was established by constructing a formal proof.
(65) The formal proof was considered groundbreaking in the field of computer science.
(66) The formal proof of the equation's solution was derived using advanced calculus.
(67) The formal proof of the conjecture was based on extensive numerical simulations.
(68) The formal proof was met with skepticism initially, but was eventually accepted.
(69) The professor guided the students in constructing a formal proof for the problem.
(70) The professor challenged the students to construct a formal proof for the theorem.
Use formal proof in a sentence
(71) The formal proof of the algorithm's correctness was provided in the documentation.
(72) The formal proof of the equation's uniqueness was established using contradiction.
(73) The researcher used a formal proof to establish the relationship between variables.
(74) The formal proof of the conjecture was finally established after years of research.
(75) The formal proof of the theorem's generalization was presented in a separate paper.
(76) The formal proof of the lemma's existence was based on the well-ordering principle.
(77) The formal proof was met with admiration and acclaim from the scientific community.
(78) The formal proof of the corollary's applicability was shown through several examples.
(79) The formal proof of the proposition's converse was left as an exercise for the reader.
(80) The formal proof of the theorem's extension was presented in a subsequent publication.
Sentence using formal proof
(81) The formal proof was presented in a step-by-step manner, leaving no room for ambiguity.
(82) The formal proof of the equation's approximation was derived using Taylor series expansion.
(83) The formal proof of the algorithm's efficiency was demonstrated through complexity analysis.
(84) The formal proof of the conjecture's impossibility was provided by a renowned mathematician.
(85) The formal proof of the lemma's optimality was demonstrated through a series of inequalities.
(86) The formal proof of the algorithm's correctness was verified using formal verification tools.
(87) The formal proof of the proposition's equivalence was established using logical equivalences.
(88) The formal proof of the conjecture's validity was established through a constructive argument.
Formal Proof meaning
Formal Proof: Tips for Using the Phrase in a Sentence The phrase "formal proof" is commonly used in the field of mathematics and logic to refer to a rigorous and systematic demonstration of the truth or validity of a statement or proposition. It is essential to understand how to use this phrase correctly in a sentence, especially in academic or professional contexts. Here are some tips to help you effectively incorporate the term "formal proof" into your writing:
1. Define the context: Before using the phrase "formal proof," it is crucial to establish the context in which you are discussing it. Clearly state whether you are referring to a mathematical proof, a logical proof, or any other specific field where formal proofs are employed. This will help your readers or listeners understand the specific meaning you intend to convey. Example: "In the field of mathematics, a formal proof is a step-by-step demonstration of the truth or validity of a mathematical statement."
2. Use it as a noun: "Formal proof" is primarily used as a noun phrase, representing the concept or process of proving something formally. It is essential to treat it as a single unit and use it accordingly in your sentence structure. Example: "The mathematician presented a formal proof to establish the validity of the theorem."
3. Be precise and concise: When using the phrase "formal proof," strive for clarity and brevity. Avoid unnecessary repetition or wordiness that may distract from the main point you are trying to convey. Example: "The formal proof provided by the researcher was concise yet comprehensive, leaving no room for doubt."
4. Provide additional information: If necessary, you can provide additional information about the specific techniques, methods, or rules employed in a formal proof. This will enhance your sentence and demonstrate your understanding of the subject matter. Example: "The student utilized axiomatic systems and logical inference rules to construct a formal proof for the given proposition."
5. Use appropriate language: Since "formal proof" is a technical term, it is essential to use appropriate language and maintain a formal tone when incorporating it into your writing. Avoid colloquial or informal language that may undermine the seriousness of the subject matter. Example: "The author's paper on formal proofs was written in a clear and concise manner, adhering to the rigorous standards of mathematical discourse."
6. Consider the audience: When using the phrase "formal proof," consider the knowledge level of your audience. If you are writing for a specialized audience, you can assume a certain level of familiarity with the term. However, if your audience is more general, it may be helpful to provide a brief explanation or definition. Example: "The lecturer explained the concept of formal proof to the audience, ensuring that even those with limited mathematical background could grasp the main ideas."
7. Connect it to broader concepts: In some cases, you may want to connect the phrase "formal proof" to broader concepts or theories within mathematics or logic. This can help situate your sentence within a larger framework and demonstrate your understanding of the subject matter. Example: "The formal proof of the theorem relied on the principles of set theory and the foundations of mathematical logic."
In conclusion, using the phrase "formal proof" correctly in a sentence requires precision, clarity, and an understanding of the specific context in which it is being used. By following these tips, you can effectively incorporate this term into your writing and communicate your ideas accurately in academic or professional settings.
The word usage examples above have been gathered from various sources to reflect current and historical usage of the word Formal Proof. They do not represent the opinions of TranslateEN.com.