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$$\int x\ dx=\int \underbrace{(1 + 1 + \cdots + 1)}_{x\text{ times}}\ dx=x^2$$ Is the algebra Ok? The professor said that the function looses continuity; could anybody explain that?

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    What does "$x$ times" mean when $x=\frac{1}{2}$?2012-09-27
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    Someone posted the question of where the error is in this argument a few weeks ago. I posted a reply. Maybe this isn't quite a duplicate question, but perhaps the same reply would work here.2012-09-27
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    Even without losing continuity this remains wrong: Compare $$\sum_{k=1}^n k =\sum_{k=1}^n \underbrace{1+1+\ldots +1}_{n} = n^2??$$2012-09-27
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    Is the problem written correctly? The integral result is wrong from the start. Was he trying to show that if you sum some set of rectangles you get the same results? Regardless, the title is wrong from the start.2012-09-27

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