Prove, for a bounded function on $[a,b]$, that if \[ \forall\epsilon\gt 0(\exists\delta\gt 0(\forall P(||P\,||\lt\delta\Rightarrow U(P)-L(P)\lt\epsilon))) \] is true, then $\phi=\Phi$.
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Lesson Parent:
Problem:
Prove, for a bounded function on $[a,b]$, that if
\[
\forall\epsilon\gt 0(\exists\delta\gt 0(\forall P(||P\,||\lt\delta\Rightarrow U(P)-L(P)\lt\epsilon)))
\]
is true, then $\phi=\Phi$.
Answer:
When \[ \forall\epsilon\gt 0(\exists\delta\gt 0(\forall P(||P\,||\lt\delta\Rightarrow U(P)-L(P)\lt\epsilon))) \] is true, then $\phi=\Phi$.
