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.
Several years later, Clarinda gained a visit back to her family in Kentucky with her children and decided to stay. They could not support her, but the state voted a 3-year pension for her. Montgomery County was established in 1796 from land given by Clark County. Montgomery was the 22nd Kentucky county in order of formation. Montgomery County was named in honor of Richard Montgomery, an American Revolutionary War Brigadier General killed in 1775 while attempting to capture Quebec City, Canada. An alternative story holds that the County was named for Thomas Montgomery from Virginia, who served in the Revolutionary War. In 1793 Thomas Montgomery settled in Mt. Sterling.