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 is currently accessed from exit 15 off Interstate 71, exit 50 off Interstate 275 and is the eastern terminus of the Ronald Reagan Cross County Highway about five miles northeast of the Cincinnati city line. The population was 10,163 at the 2000 census. Montgomery is located at 39Â°14â²50â³N 84Â°20â²51â³W / 39.24722Â°N 84.3475Â°W / 39.24722; -84.3475 (39.247359, -84.347556). According to the United States Census Bureau, the city has a total area of 5.3 square miles (13.8 kmÂ²), all of it land.