evenly continues question

f is continues in (a,b)

prove that f is not "evenly continues"
??
i dont know the proper term.

basicly we need to prove that there is so for every there is x for which and

if we choose
also we can use the limit
?

Quote:

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Originally Posted by transgalactic

f is continues in (a,b)

prove that f is not "evenly continuous"
??
i don't know the proper term.

basicly we need to prove that there is so for every there is x for which and

if we choose
also we can use the limit
?

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Do you mean: 'uniformly' continuous ?

yes

Quote:

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Originally Posted by transgalactic

f is continues in (a,b)
prove that f is not "'uniformly' continuous"???

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Do you know this theorem: If f is uniformly' continuous on a set S and is a Cauchy Sequence in S then is a Cauchy Sequence ?
You can use proof by contradiction. There is a positive integer such that .
Define . Now apply the theorem.