Epsilon-delta for a continuous function

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SUMMARY

The discussion confirms the definition of continuity for a function f: D -> R, where D is a subset of R. It states that a function f is continuous at a point a in D if, for every epsilon > 0, there exists a delta > 0 such that whenever |x - a| < delta and x is in D, it follows that |f(x) - f(a)| < epsilon. This definition is fundamental in real analysis and is essential for understanding continuous functions.

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The function f is continuous at a E R.

Let f:D->R and D be a subset of R.
The function f is continuous at a E D if for every epsilon > 0 there exists a delta > 0 so that if |x-a|< delta and x E D then: |f(x)-f(a)|< epsilon.

Can someone check this for me?
 
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that looks like the definition of continuity, is that all you wanted to know?
 
Yes, that's right.
 

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