READING:     II     1     F5                    Back to reading:     II     1     F3 and F4
begin quote ita"
CHAPTER II [:] The Real Number System [...] 1. THE FIELD PROPERTIES. "end quote
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F5:       a · 0    =    0

For any real number   a,    a·0 = 0
  a · 0  
  =  
  a · (0+0)  
  neutral element for addition  
   
  =  
  a·0 + a·0  
  distributive property of mulitplication over addition  
  but also:  
   
   
   
  a · 0    
  =  
  0 + a·0  
  neutral element for addition  
  and:  
   
   
  Both the previous row and the second row are of the form  
  a · 0  
  =  
  x + a·0  
  So we have the desired result by F3.  

on to F6