Another simple proof of the non-field-ness of floating point numbers. in this case for the IEEE "double precision" type, that associativity doesn't hold: >

Another simple proof of the non-field-ness of floating point numbers. in this case for the IEEE "double precision" type, that associativity doesn't hold: >>> a, b, c = 2 ** -53, 2 ** -53, 1 >>> (a+b)+c == a+(b+c) # definition of associativity False