Why isn't dividing by zero = zero? In layman terms, why is x divided by 0 equal to undefined, and not 0? If anything slightly above 0 is +infinity, and anything slightly below 0 is infinity, can't we argue that the number in between both infinities is 0? 
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More specifically, if you consider a function $\displaystyle f(x) = \frac{g(x)}{x}$ and then try and find the limit of that function as x tends to zero, then the limit obtained is not always zero. It changes depending on what g(x) is. A typical example is $\displaystyle g(x) = \sin x$. If you look at the attached table, which shows somes evaluations of the function with decreasing values of x, the function tends towards 1, not 0. 
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4 apples divided by 2: Jim and Joe get 2 each 4 apples divided by 1: Jim gets 4 4 apples divided by nobody: ? 
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\begin{array}{c  c} x & \frac{\sin x}{x} \\ \hline 0.1\phantom{000} & 0.998334166468282 \\ 0.01\phantom{00} & 0.999983333416667 \\ 0.001\phantom{0} & 0.999999833333342 \\ 0.0001 & 0.999999998333333 \end{array} 
Hey guys, has anyone noticed the date of the first and last posts by the martian OP? 
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