Why zero divided by zero is not 1?

Answer 1

A division is the answer to a multiplication problem. For example:

(number) = 6 / 3

is the answer to:

2 times (number) = 6

What number do you have to replace here? There is exactly one solution, namely the number 3.

1 / 0 is equivalent to:

(number) times 0 = 1.

This has no solution.

0 / 0 is equivalent to:

(number) times 0 = 0

This has infinitely many solutions; any real number will work. However, in both cases (non-zero divided by zero, and zero divided by zero), it has been shown that dividing by zero causes lots of errors (for example, you can "prove" that 0 = 1; meaning, you can "prove" almost anything, if you carelessly divide by zero). Therefore, division by zero is usually not considered an acceptable operation, especially in pure mathematics.