# Can be split 17

## Division by 0

If you divide zero by any number, you always get zero. However, if you try to divide by zero, you will get messages like 'NaN', 'nDef' or simply 'not defined', depending on the calculator. But why?

You can easily imagine this with a cookie: if there is nothing left, it can no longer be shared. Division by zero, however, is more complicated. So let's look at what happens when we divide our cookie into smaller and smaller pieces, that is, we keep getting closer and closer to zero.

surgery | Result |
---|---|

1÷2 | 0,5 |

1÷1 | 1 |

1÷0,5 | 2 |

1÷0,25 | 4 |

1÷0,05 | 20 |

1÷0,005 | 200 |

1÷0,0001 | 10.000 |

1÷0,00001 | 100.000 |

1÷0,000001 | 1.000.000 |

1÷0,0000001 | 10.000.000 |

1÷0,00000001 | 100.000.000 |

1÷0,000000001 | 1.000.000.000 |

1÷0,0000000001 | 10.000.000.000 |

1÷0,00000000001 | 100.000.000.000 |

1÷0,000000000001 | 1.000.000.000.000 |

1÷0,0000000000001 | 10.000.000.000.000 |

You can see that the closer we get to dividing by zero, the greater the result of the division. But what does this mean for dividing by zero?

As we know, division is closely related to multiplication. If I divide 1 by 2 I get 0.5. If I take 0.5 times 2, I get 1. Division and multiplication are again **inverse operations**, they basically have the opposite effect. The only problem is, if dividing by zero were theoretically possible and I took the result again from 0, I would get 0 again and again.

The limit for dividing by 0 then looks like this:

This also confirms that dividing by 0 is not possible. The closer we get to zero, the larger the quotient becomes. Infinity ∞ is not a number. If we were to divide by 0 and we got infinity as the result, we couldn't multiply the whole thing back to the starting value.

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