Browsing category proof

Attack of the Mathematical Zombies: $1=2$

"One equals two" growled the mass of zombies in the distance. "One equals two." The first put down the shotgun. "I've got this one," he said, picking up the megaphone. "If you're sure," said the second. "I'M SURE." The second covered his ears. "SORRY. I mean, sorry." The first redirected

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Ask Uncle Colin: Is my friend crazy?

Dear Uncle Colin, A friend of mine told me that $1 + 2 + 4 + 8 + ... = -1$. Is he crazy, or is there something going on here? -- Somehow Enumerating Ridiculous Infinitely Extended Sum Dear SERIES, There are a couple of 'proofs' of this non-fact that

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Ask Uncle Colin: a proof with logs in

Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions -- and to show off your skills at coming up with clever acronyms. Send your questions to colin@flyingcoloursmaths.co.uk and Uncle Colin will do what he can. Dear Uncle Colin, I have a slightly embarrassing problem: I

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A “Proof” that 1 = 2

It’s usually quite simple to spot the error in ‘proofs’ that $1=2$: either someone’s divided by 0 or glossed over inverting a multi-valued function (conveniently forgetting the second square root, for example). You sometimes (as with the sum of natural numbers being $-\frac{1}{12}$, if you throw out all good sense)

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Why does $x^3 e^{-x}$ go to zero as $x$ goes to infinity?

A student asks: I know that $x^3 e^{-x}$ approaches zero as $x$ approaches infinity - I can see it from the graph - but I don't really understand why? Can you help? Of course I can! However, it's going to take us into the murky depths of analysis, and we'll

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Why I don’t buy that $1 + 2 + 3 + … = -\frac{1}{12}$

Thanks to Robert Anderson for the question. I told him that the sum of an infinite number of terms of the series: 1 + 2 + 3 + 4 + · · · = −1/12 under my theory. If I tell you this you will at once point out to

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BREAKING NEWS: Largest prime discovered

39,916,801 has just been discovered to be the largest prime number. $11$ is a positive integer such that $11! + 1$ is prime; let $n = 11!$. Now, $n+2$ is clearly a multiple of 2, $n+3$ is a multiple of 3 and so on up to $2n$. Applying a similar

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A Co-Proof of the Birthday Problem

“[In this context] Co- just means ‘opposite’ — so a co-mathematician is a machine for turning theorems into ffee.” — Miles () Matt Parker () laid down a challenge on Day 1 of the MathsJam conference: he said that proof by MathsJam was acceptable, because if it wasn’t true, you

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How to do a trigonometry proof: five top tips

First up, a horrible confession: I like teaching the higher-lever core maths modules (C3 and C4), because they're closer to 'real' maths than the AS-level ones. One of the things that sets them apart is the introduction of proofs, usually for trigonometry1. And a lot of students struggle with it

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How to do a trigonometry proof: five top tips

First up, a horrible confession: I like teaching the higher-lever core maths modules (C3 and C4), because they're closer to 'real' maths than the AS-level ones. One of the things that sets them apart is the introduction of proofs, usually for trigonometry1. And a lot of students struggle with it

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