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Book of Proof - Third Edition - Open Textbook Library
1. Sets. 2. Logic. 3. Counting. II How to Prove Conditional Statements. 4. Direct Proof. 5. Contrapositive Proof. 6. Proof by Contradiction. III More on Proof. 7. Proving Non-Conditional Statements. 8. Proofs Involving Sets. 9. Disproof. 10. Mathematical Induction. IV Relations, Functions and Cardinality.
Mathematical Logic and Proofs - Mathematics LibreTexts
Mathematics is really about proving general statements via arguments, usually called proofs. As you no doubt know from arguing with friends, not all arguments are good arguments. A “bad” argument is one in which the conclusion does not follow from the premises, i.e., the conclusion is not a consequence of the premises.
3: Constructing and Writing Proofs in Mathematics
In essence, a proof is an argument that communicates a mathematical truth to another person (who has the appropriate mathematical background). A proof must use correct, logical reasoning and be based on previously established results. These previous results can be axioms, definitions, or previously proven theorems.
Mathematical Proofs - Stanford University
Our First Proof! 😃 Theorem: If n is an even integer, then n2 is even. Proof:Let n be an even integer. Since n is even, there is some integer k such that n = 2k. This means that n2 = (2k)2 = 4k2 = 2(2k2). From this, we see that there is an integer m (namely, 2k2) where n2 = 2m. Therefore, n2 is even. Notice how we use the value of k that we obtained above.
2.13: Introduction to Proofs - K12 LibreTexts
Two-Column Proofs; Review; Review (Answers) Vocabulary; Additional Resources; Use two column proofs to assert and prove the validity of a statement by writing formal arguments of mathematical statements. Also learn about paragraph and flow diagram proof formats.
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