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Line 23: − +
→More precise definition: Spelling, Grammar, and General Cleanup, typos fixed: contiuous → continuous
:For every ε > 0, there is a δ > 0 such that, whenever <math>0 < |x-X| < \delta, |f(x)-f(X)| < \varepsilon\,</math>
:For every ε > 0, there is a δ > 0 such that, whenever <math>0 < |x-X| < \delta, |f(x)-f(X)| < \varepsilon\,</math>
In the example in the picture on the right, the function is not contiuous at x=2. We have f(2) = 1, but it isn't continuous there. To see this, let ε=1. We would need to find δ such that
In the example in the picture on the right, the function is not continuous at x=2. We have f(2) = 1, but it isn't continuous there. To see this, let ε=1. We would need to find δ such that
:whenever <math>0 < |x-2| < \delta, |f(x)-1| < 1\,</math>
:whenever <math>0 < |x-2| < \delta, |f(x)-1| < 1\,</math>
But for all x with 2 < x < 2.1, we have
But for all x with 2 < x < 2.1, we have