Proof: f(x) = |x| is Continuous using Epsilon Delta Definition | Real Analysis Exercises

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We prove that f(x)=|x|, also known as f(x)=abs(x), the absolute value function, is continuous on the real numbers. We complete this proof using the epsilon delta definition of continuity of a function at a point. To do this, we simply take an epsilon greater than 0 and an arbitrary point c from our domain, then go through the motions of finding a delta greater than 0 so that any x in R that is within delta of c has an image within epsilon of c's image. We'll need the reverse triangle inequality theorem and not much else! Let me know if there are more epsilon delta continuity proofs you want to see!

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Reverse triangle inequality!
Brilliant! 😁

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