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}
  .
Nevertheless, abstract algebra can consider the field with one element, which is not a singleton and is not a set at all. 1 is the most common leading digit in many sets of data, a consequence of Benfords law. 1 is the only known Tamagawa number for a simply connected algebraic group over a number field.