Undefined and Zero
I know that 2/0 is undefined, but what about 0/0? You could
rewrite it as 0x=0, which would mean 0/0 is equal to all numbers.
Furthermore, using algebra you can transform the vertical line equation x
= 2 into y = (x-2)/0, which works perfectly. Is this true, or am I making
some fundamental mistake?
You have recognized that 0/0 is a very special number. By the definition of
division, it specifies the number of times you need to subtract zero from
zero until you reach zero. This, of course, can be any number at all, as
you see. Other related constructions such as 5/0, -0.1/0, etc. are truly
undefined - there are absolutely no numbers that satisfy the definition of
the operation of division for them.
Richard E. Barrans Jr., Ph.D.
PG Research Foundation, Darien, Illinois
x = 2 does not imply anything about y.
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Update: June 2012