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Bookmark or Share- Mathematical proof - WikipediaProofs employ logic expressed in mathematical symbols, along with natural language which usually admits some ambiguity. In most mathematical literature, proofs are written in terms of rigorous informal logic. Purely formal proofs, written fully in symbolic language without the involvement of natural language, are considered in proof theory.
- Book of Proof - Third Edition - Open Textbook Library1. 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.
- Introduction to mathematical arguments - University of California, BerkeleyIntroduction to mathematical arguments. (background handout for courses requiring proofs) by Michael Hutchings. A mathematical proof is an argument which convinces other people that something is true. Math isn’t a court of law, so a “preponderance of the evidence” or “beyond any reasonable doubt” isn’t good enough.
- Mathematical Logic and Proofs - Mathematics LibreTextsMathematics 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.
- Mathematical Proofs - Stanford UniversityOur 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.
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