Strongly and strictly increasing utility functions What's the difference between Strongly and strictly increasing utility functions?

What I know is that if $x'&gt;&gt;x $ where $x'$ has all elements strictly greater than $x$ then $U(x')&gt;U(x)$, I think this is the definition of Strictly increasing utility function. And if $x'&gt;&gt;x$ , 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.
The term strongly increasing function is non-standard in economics (and I believe also in math) and should have been clearly defined in the main text.

The following definitions are given only in their Appendix 1, p. 529 (2011, 3rd edition):



As the following text states:


  a strictly increasing function need not be strongly increasing, but every strongly increasing function is strictly increasing