Why are we using t = min here and not t = max? If we take the union of the two sets then wouldnt we want to choose the largest radius to make sure we stay outside of the border for the limit point when taking the union? I would have understood it if it was an intersection instead
Yes I think I understand now, I think I got a bad mental visualisation of the problem and was mistaken with not realising that the two points should be completely disjoint from each set E and F and the neighborhood according to the radius should also be completely disjoint from both sets, so a smaller radius is clearly more desireable in case the other radius starts reaching into the other set. Thank you for the help!
No problem!