They are assumed to be true at all times! All mathematical theorems are derived from definitions. Definitions are the starting points of all mathematical reasonings. We refer to true (T) or false (F) as the truth value of the statement.Ī definition is an exact, unambiguous explanation of the meaning of a mathematical word or phrase. Subsection 2.1 Statements Definition 2.1Ī statement is a declarative sentence that is either true or false but not both. ![]() To construct proofs, we will need our own vocabulary and grammar. A convincing justification is called a proof and that is what you will learn to construct for the rest of this class. A convincing justification not only needs to convince a Fields Medalist but also math major students, or anyone who has the backgrounds of the context. Whether a justification is convincing or not should not depend on who came up with it. ![]() Hopefully you get a taste of what it means by "convincing justifications" in Task 1.1.
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