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Can 0 be divided into anything?

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4 Answers

Another way to see why this is true:  try dividing by a very small number.  For example:  2/0.001 = 2000.  Now make that denominator even smaller:  2/0.0001 = 20,000.  And smaller:  2/0.0000001 = 20,000,000.

As you can probably tell by now, as the denominator gets smaller and shrinks towards zero, the quotient (the answer) grows larger, towards infinity.  So technically speaking, you can say that dividing anything by zero = infinity, and that's "undefined" (can't put a number on it) in math.  

Here is an even simpler way to see that you can't divide by zero.

Let x be a real number. and define y=x/0. By definition of division, we get 0y = x. The left hand side of this last equation equals 0 because of multiplication by zero. Thus this equation will be only true if x = 0. This means that for x ≠ 0, the expresson x/0 is automatically undefined.

In the special case of x = 0, the last equation, 0y = x holds true, for all real y. Therefore if we consider defining 0/0, we find that all real numbers work equally well. As a result, the expression 0/0 is called indeterminate. By themselves with no context, indeterminate numbers are undefined.

There are seven expressions total that are recognized as indeterminate:

0 / 0       ∞ / ∞       0 · ∞        ∞ - ∞      ∞0        1∞        00

You will learn them when you take calculus, as they arrise when taking limits.