component of the proof

USAGE SUMMARY

The phrase "component of the proof" is correct and usable in written English.
It can be used when discussing a specific part or element that contributes to the overall validity of a proof in mathematics or logic. Example: "The theorem is established by examining each component of the proof in detail."

✓ Grammatically correct

Science

News & Media

Academia

Human-verified examples from authoritative sources

Exact Expressions

2 human-written examples

The figure on the left shows a component of the proof for dimensions 3 and higher.

Princeton University

A key component of the proof of the next theorem is the following lemma.

Fixed Point Theory and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

58 human-written examples

A checkers hobbyist has independently verified major components of the proof with another computer program.

The New York Times - Science

One of the main components of the proof is a Grauert-type theorem for "holomorphic" vector bundles defined on maximal ideal spaces of certain Banach algebras.

Journal of Functional Analysis

Part of the proof will come from using standard components and procedures.

Fusion Engineering and Design

Since the first principal component of the morphometric dataset proofed to be mainly influenced by the standard length, it was not used for analysis.

BMC Evolutionary Biology

Section 3 is devoted to show that there are at least two direction turns of the component and complete the proof of Theorem 1.1.

Boundary Value Problems

Therefore we can reason in each coarse connected component as in the proof of Lemma 2.6.

Bulletin of Mathematical Sciences

Here was proof — proof that as a component of "the media," the liberal blogosphere is as important to the Democratic Party as CNN or MSNBC.

The New Yorker

The intake spark arrestor is a key component of the air intake system in explosion-proofing the diesel engine, which directly affects engine performance.

International Journal of Coal Science & Technology

We also provide a proof-of-concept instantiation of a critical component of the Experience Exchange model, the Experience Exchange Library.

Information Sciences

Expert writing Tips

Best practice

When discussing mathematical or logical arguments, use "component of the proof" to clearly identify a specific section or step that contributes to the overall validation. Ensure each component is well-defined and contributes logically to the final conclusion.

Common error

Avoid using "component of the proof" when referring to aspects that are merely related to the topic but do not directly contribute to the logical steps or evidence of the proof. Be specific in identifying genuine components.

Linguistic Context

The phrase "component of the proof" serves as a noun phrase, identifying a specific element or aspect that constitutes a part of a logical or mathematical demonstration. Ludwig AI indicates that it's grammatically correct and readily usable in written English.

Expression frequency: Uncommon

Frequent in

Science

40%

Academia

30%

News & Media

15%

Less common in

Wiki

5%

Formal & Business

5%

Encyclopedias

0%

Ludwig's WRAP-UP

In summary, the phrase "component of the proof" is a grammatically sound and clear way to refer to a constituent element of a logical argument or mathematical demonstration. As Ludwig AI confirms, it's appropriate for use in written English, particularly in formal and scientific contexts. While alternatives like "element of the proof" or "part of the proof" exist, the best choice depends on the specific emphasis desired. It's crucial to use the phrase accurately, ensuring that the identified component genuinely contributes to the validity of the proof. Its function is to dissect and examine complex arguments, highlighting the importance of precision and clarity in logical reasoning and also as "element of the proof" or "part of the proof".

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

element of the proof

Replaces "component" with "element", emphasizing a basic part.

part of the proof

Uses "part" instead of "component", indicating a section or piece.

aspect of the proof

Substitutes "component" with "aspect", focusing on a particular feature.

piece of evidence in the proof

Rephrases "component" as a specific "piece of evidence", highlighting its evidentiary role.

building block of the proof

Uses "building block" to convey the idea of a fundamental, structural element.

key ingredient of the proof

Employs "key ingredient" to emphasize the essential nature of the component.

constituent of the proof

Replaces "component" with "constituent", indicating a composing element.

factor in the proof

Uses "factor" instead of "component", focusing on a contributing cause.

cornerstone of the proof

Substitutes "component" with "cornerstone", suggesting a foundational element.

essential feature of the proof

Rephrases "component" as an "essential feature", emphasizing its importance.

FAQs

What does "component of the proof" mean in mathematical terms?

In mathematics, a "component of the proof" refers to a specific element, step, or argument that is essential for establishing the validity of a theorem or statement. Each "element of the proof" must logically contribute to the final conclusion.

How can I use "component of the proof" in a sentence?

You can use "component of the proof" to highlight a particular aspect of a demonstration. For example, "The inductive step is a crucial "part of the proof", as it extends the result to all natural numbers."

What are some alternatives to saying "component of the proof"?

Alternatives include "element of the proof", "aspect of the proof", or "part of the proof". The choice depends on whether you want to emphasize a basic part, a specific feature, or a section of the demonstration.

Which is more appropriate, "component of the proof" or "element of the proof"?

Both "component of the proof" and "element of the proof" are appropriate and largely interchangeable. "Element" might suggest a more fundamental or basic aspect, while "component" implies a contributing piece within a larger structure. Therefore, using either "component of the proof" or "element of the proof" depends on the specific context.