Since this is true for any points x and y within the set that we might choose, the set is convex. Illustration of a non-convex set. Since the red part of the (black and red) line-segment joining the points x and y lies outside of the (green) set, the set is non-convex.
Montgomery County is a county in the U.S. state of Texas. As of the 2010 census, its population was 455,746. A 2013 estimate places the population at 499,137. The county seat is Conroe. The county was created by an act of the Congress of the Republic of Texas on December 14, 1837 and is named for the town of Montgomery. Between 2000 and 2010, its population grew by 55%, the 24th-fastest rate of growth of any county in the United States.
It had its beginning not long after the town of Montgomery, because in the Telegraph and Texas Register of April 8, 1846, it was listed as one of the towns of Montgomery County for election returns of that year. 31 During the 1850's, Danville, like Montgomery, had a building boom.