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.
Welcome to the City of Montgomery. As one of the oldest towns in Texas, Montgomery began as a trading post in 1826 and was charted in 1837. Montgomery was the first county seat of Montgomery County and was the third county formed under the Republic of Texas. It is also recognized as the birthplace of the Texas Lone Star Flag. Montgomery is located at the junction of Texas 105 and FM 149, near the southwestern edge of Sam Houston National Forest in western Montgomery County. The center of town is 15 miles west of Conroe and 50 miles northwest of Houston.