There are no 2 x 2 magic squares; they also can be defined as the only null 
  
    
      
        n
      
    
    {\displaystyle n}
   by 
  
    
      
        n
      
    
    {\displaystyle n}
   magic square set.Two also has the unique property such that,

  
    
      
        
          ∑
          
            k
            =
            0
          
          
            n
            −
            1
          
        
        
          2
          
            k
          
        
        =
        
          2
          
            n
          
        
        −
        1
      
    
    {\displaystyle \sum _{k=0}^{n-1}2^{k}=2^{n}-1}
  and also, with a not equal to zero,

  
    
      
        
          ∑
          
            k
            =
            a
          
          
            n
            −
            1
          
        
        
          2
          
            k
          
        
        =
        
          2
          
            n
          
        
        −
        
          ∑
          
            k
            =
            0
          
          
            a
            −
            1
          
        
        
          2
          
            k
          
        
        −
        1
      
    
    {\displaystyle \sum _{k=a}^{n-1}2^{k}=2^{n}-\sum _{k=0}^{a-1}2^{k}-1}
  .In any n-dimensional, euclidean space two distinct points determine a line.
{\displaystyle \sum _{k=0}^{\infty }{\frac {1}{n^{k}}}=1+{\frac {1}{n-1}}\quad {\mbox{for all}}\quad n\in \mathbb {R} >1.} A Cantor space is a topological space 
  
    
      
        
          2
          
            
              N
            
          
        
      
    
    {\displaystyle 2^{\mathbb {N} }}
   homeomorphic to the Cantor set. The countably infinite product topology of the simplest discrete two-point space, {0, 1}, is the traditional elementary example. The sum of the reciprocals of all non-zero triangular numbers converges to 
  
    
      
        2
      
    
    {\displaystyle 2}
  .Powers of two are central to the concept of Mersenne primes, and important to computer science. Two is the first Mersenne prime exponent.