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Message: <blockquote data-quote="spoon737" data-source="post: 1584008" data-attributes="member: 590038">1/0 is undefined.  If 1/0 = x, then 1 = 0x, implying that we could multiply some number by zero and get one, which is clearly false.  Using limits, we can analyze the behavior of the function 1/x as x gets arbitrarily close to zero, and we find that the function tends to infinity or negative infinity, depending on the sign of x.  However, this is NOT the same thing as actually dividing by zero.  First year calculus students sometimes get the misconception that limits allow us to suddenly perform operations that are illegal with normal arithmetic, but this is born out of a misunderstanding of what limits actually are.  They are merely a tool that allows us to see what a function does at values close to a particular input, but not literally at that input.So, I'll say it again.  1/0 is NOT infinity, it is just undefined.</blockquote>