I was doing a problem based on constructing an interval centered on c which is a subset of a separate interval (a,b) , where c∈(a,b) and a and b are real numbers.
The issue with trying to create an interval like I=(c−(c−a),c+(c−a)) is that c may be closer to b than to a, and thus adding the difference between c and a would exceed b, and I wouldn't be a subset of (a,b).
I was looking at the solution manual and it said: Let r=min(c−a,b−c), and let I=(c−r,c+r).
From this it seems that min means select r to be the smaller of the two numbers in the parentheses? I've never seen this operation before and it's not in the textbook. Is it just shorthand for :
Let r be an element of the real numbers : if (c−a)>(b−c) then r=b−c . If (c−a)<(b−c) then r=c−a. If (c−a)=(b−c) then r=c−a=b−c ?