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## Main Question or Discussion Point

lim 1/x as x->0 is infinity, but the function taking it to infinity is continuous, but for continous functions f(a)= lim f(x) as x->a, so by defininition 1/0 is infinity, what is wrong with this logic?

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- #1

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lim 1/x as x->0 is infinity, but the function taking it to infinity is continuous, but for continous functions f(a)= lim f(x) as x->a, so by defininition 1/0 is infinity, what is wrong with this logic?

- #2

pwsnafu

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- #3

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a is 0, f=1/x

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pwsnafu

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Yeah, sorry. I realised and edited my post. You replied just before I finished.a is 0, f=1/x

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oh, 1/x, x element of R, and inf not element of R but cardinality, thanks.

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pwsnafu

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is not true. The left and right limits are not the same.lim 1/x as x->0 is infinity

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Why not? 1/x coming from the negative side to 0 should yield same result as from the positive?Also, I want to point out

is not true. The left and right limits are not the same.

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No.The limit from the left is ##-\infty##. For example ##1/(-.01) = -100##Why not? 1/x coming from the negative side to 0 should yield same result as from the positive?

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mfb

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There is no way to extend the definition of f to x=0 in a continuous way.but for continous functions f(a)= lim f(x) as x->a

- #10

Mark44

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Take a look at the graph of y = 1/x. There is the worst possible kind of discontinuity at x = 0, with ##\lim_{x \to 0^-} \frac 1 x = -\infty## and ##\lim_{x \to 0^+} \frac 1 x = +\infty##.lim 1/x as x->0 is infinity, but the function taking it to infinity is continuous, but for continous functions f(a)= lim f(x) as x->a, so by defininition 1/0 is infinity, what is wrong with this logic?