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I was reading through some lecture notes on Single-Variable Calculus, and the teacher gave this definition of continuity:

"A function f is called continuous at a point p if a value f(p) can be found such

that f(x) → f(p) for x → p. A function f is called continuous on [a, b] if it is

continuous for every point x in the interval [a, b]."

Now, I thought this meant the function actually had to be defined at p, but the teacher says that the function 1/log(|x|) is continuous at 0. Of course, log(|x|) isn't defined at 0. So, I have to ask the question, Does a function have to be defined at a point to be continuous at that point?

Thanks,

Mathguy

PS: I have found other definitions that say f(p) must exist.

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# Really Basic Question regarding Continuity

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