Absolute Proof that  IS NOT EQUAL TO   A mathwiki  You are wrong about infinite representation The ancient Greeks never represented  as    Now let me refute your argument regarding the transitive property  A     B       C        The problem here occurs in B where you assume that        You have not proved anything On the contrary you have only proved that you are assuming    which it is obviously not equal  is an indeterminate number because it cannot be represented finitely in base    is not equal to  so you cannot say that  is a finite representation An indeterminate number is a number that is repeating in any radix system  You mention the division algorithm but do you know what it says The division algorithm has nothing to do with radix systems Let me state it for you  If a and b are two given integers there are unique integers q and r such that abq  r and   r  b Now I will use the division algorithm to prove that you are WRONG once and for all Suppose a   and b   then  what are the integers q and r such that the above is true  Suppose that q   and r   Then the division algorithm fails because it makes a false statement ie q and r can both be  and  respectively For example    and    So by default the division algorithm is proved false if  is equal to  And you can say a lot of things about the Greeks but they would not make a stupid mistake like this They were the smartest race in ancient times  Now suppose that you try to tell me that either form is acceptable in the case of  and  you will still end up with a terrible contradiction   The second form in this case implies that    since r  b But how can  be less than    I want the world to know what fg idiots run this site You are a bunch of retarded conceited fools who I look upon with the utmost hatred and condemnation Your site is absolute crap because it is run by fools like Michael Hardy Kmrsq Melchoir Meni idiot Rosenfeld et al DIE WIKIPEDIA HAIL KNOLL