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Forum index » Science and Technology » Math » Undergraduate
f continuous at b, f(b) <> c
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G.E. Ivey
science forum Guru


Joined: 29 Apr 2005
Posts: 308

PostPosted: Sun Jun 25, 2006 5:28 pm    Post subject: Re: f continuous at b, f(b) <> c Reply with quote

Let epsilon= |f(b)-c|/2
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Romeo Colacitti
science forum beginner


Joined: 29 Apr 2005
Posts: 36

PostPosted: Sun Jun 25, 2006 2:52 am    Post subject: f continuous at b, f(b) <> c Reply with quote

If f is continuous at b and f(b) <> c, can I conclude that:

there is an open interval containing b, such that f <> c on that open
interval ?

If yes, why is it so? I have a "gut" feeling, but can't provide myself
a proof.
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