The discussion revolves around proving the continuity of a function \( f \) defined on the interval \( (a,b) \) under the condition that \( |f(x) - f(t)| \leq |x - t| \) for any points \( x \) and \( t \) in that interval.
The discussion is ongoing, with participants seeking clarification on the definition of continuity and how to structure a proof. Some have suggested writing down a precise definition and considering the relationship between epsilon and delta.
There is uncertainty regarding the specific requirements of the proof, as some participants express confusion about the expectations set by the problem statement.
Dr. Science said:Homework Statement
Suppose that a function f has the property that
|f(x) - f(t)| < or = |x-t| for each pair of points in the interval (a,b). Prove that f is continuous
on (a,b)
Homework Equations
?
The Attempt at a Solution
f(x) and f(t) must be defined everywhere on (a,b)