Mistakes

The Gambler’s Fallacy

Probability seems simple enough to many people that it can fool them into wrong conclusions. We have had many questions that involve the “Gambler’s Fallacy”, both from people who naively assume it without thinking, and from some who defend it using technical ideas like the Law of Large Numbers. The Gambler’s Fallacy Here is a …

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1=0? Calculus Says So [or Not]

“False Proofs”, where seemingly good logic leads to nonsensical conclusions, can be a good way to learn the boundaries of reality — what to look out for when you are doing real math. We have a FAQ on the subject; there we discuss several well-known fallacies based in algebra, and have links to others. Today, …

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When Can a Function Equal Its Inverse?

(New Question of the Week) This week I answered a seemingly simple question that can be solved in several different ways when presented as multiple choice, but is rather difficult as a straightforward algebra problem. Trying to guess what the “patient” had done yielded an invalid method that gave the right answer — or was it really invalid? …

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