What's the difference between Strongly and strictly increasing utility functions?
What I know is that if $x'>>x $ where $x'$ has all elements strictly greater than $x$ then $U(x')>U(x)$, I think this is the definition of Strictly increasing utility function. And if $x'>>x$ , then $U(x')\geq U(x)$, this is the definition of Increasing function(monotone) function. I've no idea about Strongly Increasing function. Can anyone show a graphical example if this strongly increasing assumption is violated, how will the graph look like? (Utility function's graph)
Reference is from GEOFFREY A. JEHLE PHILIP J. RENY, Advanced Microeconomic Theory.