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okay so here in this problem this is the lower envelope what were given is a set unsorted unordered of n lines in the plane so theyre just some messy I know ordered they go to infinity of both directions this one ends up intersecting over there thats not these guys go after there and maybe theres another one here okay so the lower envelope is the least the lowest point on the set of lines as you span from left to right minus infinity to positive infinity so in this little example the lower envelope goes this way and each one of these points is called a break point so this lower envelope has one two three four line segments and three break points so is that clear by example what a lower envelope of a set of n lenses say what well theres a little segment in here yeah its its hard to see probably the ones in livermore have trouble but theres a little segment and here between two break points how many lower envelopes just one well this is these lines go to infinity in both directi