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Name: Etienne
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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.
Assistant Director
PG Research Foundation, Darien, Illinois

x = 2 does not imply anything about y.

Tim Mooney

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