What is the meaning of c = min {a, b/M} in IVP proofs?

[hawkingfan]

Hey dudes, I'm trying to understand the proofs about IVPs in the appendix of my differential equations book but I can't understand this notation that says c = min {a, b/M}.

What is that notation supposed to mean? I'm guessing that it stands for minimum value between a and b/m. (a is associated with the x-axis and b/M is associated with the y-axis based on the picture of the graph in the book) I'm just beginning to study real analysis so I haven't seen this notation yet.

 

[nicksauce]

Yes it just means to take the minimum value between a and b/M.

In general x = min{y1,y2,y3,...,yn} means to take the minimum value from the set {y1,y2,y3,...,yn}.

 

[Hurkyl]

"min S" is the element of S that is less than every other element -- it's minimum.

(the domain of "min" consists only of those ordered sets with a minimum. In other words, if S doesn't have a minimum, then "min S" is undefined)