{\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.
The number of up-arrows refers to the level of the hyperoperation. Two is the only number x such that the sum of the reciprocals of the natural powers of x equals itself.