- #1

- 28

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Is this statement true ? Is every increasing monotonic function in a closed interval also continuous ?

How do you prove such a thing ?

Thank you !

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- MHB
- Thread starter Lancelot1
- Start date

- #1

- 28

- 0

Is this statement true ? Is every increasing monotonic function in a closed interval also continuous ?

How do you prove such a thing ?

Thank you !

- #2

- 921

- 2

For example the function f(x)= x for \(\displaystyle 0\le x\le 1\), f(x)= x+1 for \(\displaystyle 1\le x\le 2\), and, in general, f(x)= x+ n for \(\displaystyle n\le x\le n+1\) for n an integer is monotone increasing for all x but is discontinuous at every integer.

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