The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: question on definitions
Replies: 3   Last Post: Aug 4, 2013 9:48 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
William Elliot

Posts: 2,637
Registered: 1/8/12
Re: question on definitions
Posted: Aug 4, 2013 9:48 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Sun, 4 Aug 2013, G Patel wrote:

> Some definitions I read are like follows:
> definition of continuity of a function at x:

f is continuous at x when for all open V nhood f(x),
there's some open U nhood x with f(U) subset V.

> Let f be a function defined on an open interval of x.

> Now/then, f is said to be continuous at x if/iff some predicate P(f,x) is
> true.

Too vague for an intelligent response.

> f is said to be continuous at x if/iff f is a function defined on an open
> interval of x and some predicate P(f,x) is true.

> That is, when the first statement is made ahead of the definition proper,
> how do we interpret it? If some point does not meet the initial statement,
> are we allowed to call the function "discontinuous" at that point?

That f be defined about an interval of x isn't needed except perhaps
for those doing analysis. For example f:{ 0, 1/n | n in N } -> R,
1/n -> 1/2n if n in N, 0 -> 1 is continuous at every point of the
domain of f except at 0. If instead 0 -> 0, then f is continuous.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.