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When you give reasons that something is true, but don't necessarily lay it out step-by-step, this is an informal proof. A formal proof, on the other hand, shows step-by-step statements with reasons given for each step.

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Q: What is the difference between a formal and an informal proof?
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What are the differences between formal letters and emails?

The difference between a formal letter and an email is proof of service. There is no proof of service for an email because the sender has no way to check to see if the letter was read. A formal letter can be sent with a return receipt request to make sure a person receives it. An email does not have a definite source unless the IP address of the sender is tracked. The formal letter can have a return address.


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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.


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A proof uses postulates and theorems to prove some statement.


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A proof written in the form of a paragraph (as opposed to a two-column proof)


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Which is used to reach a conclusion in a formal proof?

Deductive Reasoning.