Riders, lemmas, theorems.
Proven Theorems.. Plato ;)
Prove (verb). A prosecutor has to prove the defendant committed a crime. He presents the proof to the jury in order to prove his case.Another, job-specific verb form of proof is in my industry, journalism, where we will say "Would you proof this page?" In this case proof is a shortened version of the verb proofread. This probably is not in Webster's.
A proof is a very abstract thing. You can write a formal proof or an informal proof. An example of a formal proof is a paragraph proof. In a paragraph proof you use a lot of deductive reasoning. So in a paragraph you would explain why something can be done using postulates, theorems, definitions and properties. An example of an informal proof is a two-column proof. In a two-column proof you have two columns. One is labeled Statements and the other is labeled Reasons. On the statements side you write the steps you would use to prove or solve the problem and on the "reasons" side you explain your statement with a theorem, definition, postulate or property. Proofs are very difficult. You may want to consult a math teacher for help.
Every rational number has a decimal expansion that either terminates (like 42.23517) or repeats (like 26.1447676767676...)Pi's decimal expansion neither terminates nor repeatsHence, Pi cannot be rational.If we could prove the first two statements, this would constitute a proof that Pi is irrational, but most people cannot provide proof of either. Most proofs on this issue are quite technical, but I'm hoping to return to this question with a suitable answer soon.
With an indirect proof, you temporarily assume that the opposite of what you're trying to prove is true. For example, let's say I'm trying to prove that the sky is blue. With an indirect proof, I would first say: "Assume temporarily that sky is not blue..." and go from there. Eventually, I will reach a contradiction and with this contradiction I can assume that this route of thinking is false, therefore my proof must be true.
Proven Theorems.. Plato ;)
Prove (verb). A prosecutor has to prove the defendant committed a crime. He presents the proof to the jury in order to prove his case.Another, job-specific verb form of proof is in my industry, journalism, where we will say "Would you proof this page?" In this case proof is a shortened version of the verb proofread. This probably is not in Webster's.
A proof is a very abstract thing. You can write a formal proof or an informal proof. An example of a formal proof is a paragraph proof. In a paragraph proof you use a lot of deductive reasoning. So in a paragraph you would explain why something can be done using postulates, theorems, definitions and properties. An example of an informal proof is a two-column proof. In a two-column proof you have two columns. One is labeled Statements and the other is labeled Reasons. On the statements side you write the steps you would use to prove or solve the problem and on the "reasons" side you explain your statement with a theorem, definition, postulate or property. Proofs are very difficult. You may want to consult a math teacher for help.
A criminal conviction in court would normally require proof.
A deed would prove ownership.
You may optionally register a copyright (in some countries) as documented proof of ownership, but you generally have no obligation to prove you own it. If a defendant wants to claim you do NOT own it, they would have the burden of proof.
This is a "proof by contradiction", where the evidence would fail to support the reverse assumption, giving credence to the original hypothesis.
A person would have to submit their coin to an authentication service. Then the service would prove if the coin is real or not and give a proof of authenticity if the coin was authentic.
There IS no proof of aliens. There are a lot of tall tales told about aliens in flying saucers, but after 60 + years, there would be some proof by now, if it really were real.
Every rational number has a decimal expansion that either terminates (like 42.23517) or repeats (like 26.1447676767676...)Pi's decimal expansion neither terminates nor repeatsHence, Pi cannot be rational.If we could prove the first two statements, this would constitute a proof that Pi is irrational, but most people cannot provide proof of either. Most proofs on this issue are quite technical, but I'm hoping to return to this question with a suitable answer soon.
Tell him to be honest, respectful, treat you as an equal, and be considerate of your feelings. That would be proof enough.
Once you familiarize yourself with the basic axioms and theorems of geometry, you will be able to see how they apply to the proof of any particular problem that you may be working on.