In sports
In many professional sports, the number 1 is assigned to the player who is first or leading in some respect, or otherwise important; the number is printed on his sports uniform or equipment. This is the pitcher in baseball, the goalkeeper in association football (soccer), the starting fullback in most of rugby league, the starting loosehead prop in rugby union and the previous years world champion in Formula One. 1 may be the lowest possible player number, like in the American–Canadian National Hockey League (NHL) since the 1990s or in American football. In other fields
Number One is Royal Navy informal usage for the chief executive officer of a ship, the captains deputy responsible for discipline and all normal operation of a ship and its crew. 1 is the value of an ace in many playing card games, such as cribbage. List of highways numbered 1
List of public transport routes numbered 1
1 is often used to denote the Gregorian calendar month of January. 1 CE, the first year of the Common Era
01, the former dialling code for Greater London (now 020)
For Pythagorean numerology (a pseudoscience), the number 1 is the number that means beginning, new beginnings, new cycles, it is a unique and absolute number. PRS One, a German paraglider design
+1 is the code for international telephone calls to countries in the North American Numbering Plan.
The generating function that has all coefficients 1 is given by

  
    
      
        
          
            1
            
              1
              −
              x
            
          
        
        =
        1
        +
        x
        +
        
          x
          
            2
          
        
        +
        
          x
          
            3
          
        
        +
        …
      
    
    {\displaystyle {\frac {1}{1-x}}=1+x+x^{2}+x^{3}+\ldots }
  
This power series converges and has finite value if and only if 
  
    
      
        
          |
        
        x
        
          |
        
        <
        1
      
    
    {\displaystyle |x|<1}
  .