I need someone's help to make me clear with both definition of continuity and uniform continuity. Let's say a function is continuous on a closed interval $[a,b].$ So what I can relate from this case, if we use the definition of continuity then we can see that delta is depending on the epsilon and an element of the interval $[a,b].$ However, if the function is uniformly continuous, the delta is only depending on the epsilon. Can anyone explain the difference between both definitions? Thanks.
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1I think you mean "function" where you write "sequence". – Ethan Bolker Jun 14 '18 at 17:33
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Didn't you say the difference yourself? The delta cannot depend on the chosen point for uniform continuity. – Jun 14 '18 at 17:52