Why zero divided by zero is not 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.

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