Propositions in a Formal Mathematical Proof

When writing a mathematical proof, we need to be very precise in our communication. To do this, mathematicians use the language and notation of formal logic to communicate proofs precisely and without ambiguity. As you become more experienced writing your own proofs, you will become more familiar with the language used and the structure of a proof.

The smallest unit in a mathematical proof is a proposition, which is a statement which is either true or false, though we may not know which. A mathematical proof starts from a set of propositions whose truth or falsity is already known, which we call the proof's premise, and applies a combination of these to establish the truth or falsity of new propositions.

Formal logic is not limited to mathematical proofs only. In this section, we will explore the concepts of formal logic before we see how we can use these to represent mathematical statements.

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