The examples in the slideshow, Division by Zero, which is located in the media section of Chapter 1, indicate that there is a different answer when 0 is divided by a number, rather than when a number is divided by 0.

Yep!

0/5 = 0

5/0 is very, very very big
try on your calculator
5/ 0.00000001

To understand why there is a different answer when dividing 0 by a number compared to dividing a number by 0, let's first review the concept of division.

Division is an arithmetic operation that distributes a quantity into equal parts. When we divide a number by another number, we are essentially asking how many times the divisor can be subtracted from the dividend before reaching zero or a remainder.

Now, let's consider the case of dividing a number by 0. Mathematically, this operation is undefined. Why? Well, if we try to subtract 0 from a number repeatedly, we would never reach zero because we are not changing the quantity we are subtracting. Thus, dividing by 0 does not give us a meaningful result.

On the other hand, when we divide 0 by a number, we can think of it as asking how many times the number can be subtracted from 0 before reaching zero or a remainder. However, since we are starting with 0, we can subtract any number from it an infinite number of times without ever reaching a remainder or a non-zero value. Therefore, dividing 0 by a non-zero number yields a result of 0.

In summary:
- Division by 0 is undefined because no number can be subtracted from 0 an infinite number of times.
- Division of 0 by any non-zero number is 0 because we can subtract any number from 0 infinitely without reaching a remainder.

Please note that division by zero is not permissible in mathematics and can lead to contradictions and inconsistencies in mathematical reasoning. It is considered an error or undefined operation.