The complex numbers 
  
    
      
        
          C
        
      
    
    {\displaystyle \mathbb {C} }
   share all four multiplicative algebraic properties of the reals 
  
    
      
        
          R
        
      
    
    {\displaystyle \mathbb {R} }
  , without being ordered. The quaternions loose a further commutative algebraic property, while holding associative, alternative, and power-associative properties. The octonions are alternative and power-associative, while the sedenions are only power-associative. The sedenions and all further extensions of these four normed division algebras are solely power-associative with non-trivial zero divisors, which makes them non-division algebras.
The number of strings on a violin, a viola, a cello, double bass, a cuatro, a typical bass guitar, and a ukulele, and the number of string pairs on a mandolin. "Four calling birds" is the gift on the fourth day of Christmas in the carol "The Twelve Days of Christmas". Groups of four
Big Four (disambiguation)
Four basic operations of arithmetic: addition, subtraction, multiplication, division. Greek classical elements (fire, air, water, earth). Four seasons: spring, summer, autumn, winter. The Four Seasons (disambiguation)
A leap year generally occurs every four years. Approximately four weeks (4 times 7 days) to a lunar month (synodic month = 29.53 days). Thus the number four is universally an integral part of primitive sacred calendars. Four weeks of Advent (and four Advent candles on the Advent wreath). Four cardinal directions: north, south, east, west. Four Temperaments: sanguine, choleric, melancholic, phlegmatic. Four Humors: blood, yellow bile, black bile, phlegm. Four Great Ancient Capitals of China. Four-corner method. Four Asian Tigers, referring to the economies of Hong Kong, Taiwan, South Korea, and Singapore
Cardinal principles. Four cardinal virtues: justice, prudence, temperance, fortitude. Four suits of playing cards: hearts, diamonds, clubs, spades. Four nations of the United Kingdom: England, Wales, Scotland, Northern Ireland. Four provinces of Ireland: Munster, Ulster, Leinster, Connacht. Four estates: politics, administration, judiciary, journalism. Especially in the expression "Fourth Estate", which means journalism. Four Corners is the only location in the United States where four states come together at a single point: Colorado, Utah, New Mexico, and Arizona.