Why 1 Divided by 0 is NOT Zero (It's Something Worse)
1 divided by 0. Quick, what is it?
If you said zero, you're wrong. The answer is undefined. There is no number that satisfies it.
Here's why, in three different ways.
First, what does division actually mean? 8 divided by 2 equals 4 because 2 times 4 is 8. In general, a divided by b equals c if and only if b times c equals a. Division is multiplication, in reverse.
So 1 divided by 0 would have to be some number x where 0 times x equals 1. Try any x you want. 5? Zero. 100? Zero. A million? Zero. Zero times anything is zero. There is no number that makes 0 times x equal 1.
Second, look at the graph of 1 over x. As x approaches 0 from the right, the curve shoots up to positive infinity. As x approaches 0 from the left, it plunges to negative infinity. Two different infinities, depending on which side. There is no single value at x equals 0.
Third, just watch what happens when you make x smaller and smaller. 1 over 1 is 1. 1 over 0.1 is 10. 1 over 0.01 is 100. 1 over 0.001 is 1,000. The reciprocal blows up. There is no number waiting at the limit.
So 1 divided by 0 is not zero. It's undefined. Period.
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