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*November 28, 2009* Assume Deborah learned how to prove Modern Algebra is an awesome math class this semester. Then Deborah can write proofs. Clearly, Deborah learned how to write some types of proofs in Linear Algebra freshman year. Thus, she had the prerequisite to take Modern Algebra. However, proofs in Modern Algebra have a specific format. Since Modern Algebra-type proofs are usually composed of complete sentences that sometimes run-on but still make a little sense, and since the words "since," "thus," "therefore," "then," "so," "however," and "clearly," are usual sentence starters, then if Deborah can write Modern Algebra-type proofs, then Deborah uses those words a lot in her sentences. Clearly, Deborah uses those words a lot. Thus, since Deborah can write proofs, Deborah can write Modern Algebra proofs. If Deborah can write Modern Algebra-type proofs, then she either learned to write such proofs in Modern Algebra or Real Analysis. Thus, since Deborah learned how to prove Modern Algebra is an awesome math class this semester, Deborah is either in Modern Algebra or Real Analysis this semester. Suppose Deborah is not in Modern Algebra. Then she must have learned to write proofs in Real Analysis. However, Deborah signed up to take Real Analysis next semester, so she cannot be in Real Analysis this semester. This is a contradiction. Thus, Deborah is in Modern Algebra this semester.

Assume Deborah is in Modern Algebra this semester. Then Deborah has Professor Redfield as her Modern Algebra professor. Since Professor Redfield is her professor, then Deborah has a very helpful professor with a lot of office hours, so Deborah goes to office hours a lot this semester to get help with Modern Algebra. Since Deborah goes to office hours a lot, Deborah must have learned how to write proofs. Clearly, Deborah enjoys her Modern Algebra class, so Modern Algebra must be an awesome class. If Modern Algebra is an awesome class, and Deborah learned how to write proofs, then Deborah learned how to prove Modern Algebra is an awesome class.

Thus, Deborah learned how to prove Modern Algebra is an awesome math class if and only if Deborah is in Modern Algebra this semester.

QED

Okay, not the best proof...but you get the idea. Math is fun.

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