Proof (noun):
1. Evidence: Proof refers to evidence, facts, or information that establishes the truth or validity of a statement or proposition. It is used as a noun and is often preceded by the word "the."
- Example: "The lawyer presented concrete proof of his client's innocence."
2. Degree of Certainty: In mathematics and logic, proof refers to a formal and rigorous demonstration that establishes a mathematical theorem or proposition beyond doubt.
- Example: "The mathematician provided a detailed proof of the Pythagorean theorem."
Prove (verb):
1. Establish Truth: Prove is a verb that means to establish the truth or validity of a statement, proposition, or theory through evidence or reasoning.
- Example: "The scientist conducted experiments to prove their hypothesis."
2. Demonstrate: Prove can also mean to demonstrate or show something clearly and convincingly.
- Example: "The athlete proved their skills by winning the competition."
In summary, "proof" is a noun that refers to evidence or a demonstration of truth, while "prove" is a verb that means to establish or demonstrate the truth of something.