Taking the square root of a number is such a common mathematical operation, that the spot on the root sign where the index would normally be written for cubic and other roots, may simply be left blank for square roots, as it is tacitly understood. The square root of 2 was the first known irrational number. The smallest field has two elements. In a set-theoretical construction of the natural numbers, 2 is identified with the set {{∅},∅}. This latter set is important in category theory: it is a subobject classifier in the category of sets. Two consecutive twos (as in "22" for "two twos"), or equivalently "2-2", is the only fixed point of John Conways look-and-say function. This in contrast, for example, with "1211", which would read as "one 1, one 2, and two 1s" or "111221".
This comes from the fact that:

  
    
      
        
          ∑
          
            k
            =
            0
          
          
            ∞
          
        
        
          
            1
            
              n
              
                k
              
            
          
        
        =
        1
        +
        
          
            1
            
              n
              −
              1
            
          
        
        
        
          
            for all
          
        
        
        n
        ∈
        
          R
        
        >
        1.