Positive real numbers

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the <a href="/facts/Set_(mathematics)/BfucfHMq">set</a> of positive real numbers, 
  
    
      
        
          
            R
          
          
            >
            0
          
        
        =
        
          {
          
            x
            ∈
            
              R
            
            ∣
            x
            >
            0
          
          }
        
        ,
      
    
    {\displaystyle \mathbb {R} _{>0}=\left\{x\in \mathbb {R} \mid x>0\right\},}
  
 is the subset of those <a href="/facts/Real_number/R02gw5Pb">real numbers</a> that are greater than zero. The non-negative real numbers, 
  
    
      
        
          
            R
          
          
            ≥
            0
          
        
        =
        
          {
          
            x
            ∈
            
              R
            
            ∣
            x
            ≥
            0
          
          }
        
        ,
      
    
    {\displaystyle \mathbb {R} _{\geq 0}=\left\{x\in \mathbb {R} \mid x\geq 0\right\},}
  
 also include zero. Although the symbols 
  
    
      
        
          
            R
          
          
            +
          
        
      
    
    {\displaystyle \mathbb {R} _{+}}
  
 and 
  
    
      
        
          
            R
          
          
            +
          
        
      
    
    {\displaystyle \mathbb {R} ^{+}}
  
 are ambiguously used for either of these, the notation 
  
    
      
        
          
            R
          
          
            +
          
        
      
    
    {\displaystyle \mathbb {R} _{+}}
  
 or 
  
    
      
        
          
            R
          
          
            +
          
        
      
    
    {\displaystyle \mathbb {R} ^{+}}
  
 for 
  
    
      
        
          {
          
            x
            ∈
            
              R
            
            ∣
            x
            ≥
            0
          
          }
        
      
    
    {\displaystyle \left\{x\in \mathbb {R} \mid x\geq 0\right\}}
  
 and 
  
    
      
        
          
            R
          
          
            +
          
          
            ∗
          
        
      
    
    {\displaystyle \mathbb {R} _{+}^{*}}
  
 or 
  
    
      
        
          
            R
          
          
            ∗
          
          
            +
          
        
      
    
    {\displaystyle \mathbb {R} _{*}^{+}}
  
 for 
  
    
      
        
          {
          
            x
            ∈
            
              R
            
            ∣
            x
            >
            0
          
          }
        
      
    
    {\displaystyle \left\{x\in \mathbb {R} \mid x>0\right\}}
  
 has also been widely employed, is aligned with the practice in algebra of denoting the exclusion of the zero element with a star, and should be understandable to most practicing mathematicians.
</p><p>In a <a href="/facts/Complex_plane/vE0QrxJp">complex plane</a>, 
  
    
      
        
          
            R
          
          
            >
            0
          
        
      
    
    {\displaystyle \mathbb {R} _{>0}}
  
 is identified with the positive real axis, and is usually drawn as a horizontal <a href="/facts/Ray_(geometry)/gJqsr4Gj">ray</a>. This ray is used as reference in the <a href="/facts/Complex_number/2w7mqI7e">polar form of a complex number</a>. The real positive axis corresponds to <a href="/facts/Complex_number/2w7mqI7e">complex numbers</a> 
  
    
      
        z
        =
        
          |
        
        z
        
          |
        
        
          
            e
          
          
            
              i
            
            φ
          
        
        ,
      
    
    {\displaystyle z=|z|\mathrm {e} ^{\mathrm {i} \varphi },}
  
 with <a href="/facts/Argument_(complex_analysis)/JSjfxb5U">argument</a> 
  
    
      
        φ
        =
        0.
      
    
    {\displaystyle \varphi =0.}

</p>

Positive real numbers open-in-new

Positive real numbers