>>14013508Short answer: Because 0 ÷ 0 could be anything
Long answer:
The concept of division naturally comes up when trying to undo multiplication.
Let's say I had a secret number and I completely forgot what it was. However, I remember that when I multiplied that secret number by 3, I got 12.
Can you work backwards to figure out what my secret number must have been? In this case, my secret number must have been 4. 4 × 3 does in fact give me 12 and no other number times 3 gives 12.
One potential interpretation of 12 ÷ 3 could be "The number that when multiplied by 3, gives you 12". With that interpretation, I think we can all agree that 12 ÷ 3 is 4.
Let's say I had a secret number and I completely forgot what it was. However, I remember that when I multiplied that secret number by 0, I got 0.
Can you work backwards to figure out what my secret number must have been? In this case, my secret number could have been anything.
One potential interpretation of 0 ÷ 0 could be "The number that when multiplied by 0, gives you 0". But that's an ambiguous statement. There are many such numbers. Which one do you mean when you say "the"?
Let's say I had a secret number and I completely forgot what it was. However, I remember that when I multiplied that secret number by 0, I got 5.
Can you work backwards to figure out what my secret number must have been? In this case, something went wrong. No such number exists.
One potential interpretation of 5 ÷ 0 could be "The number that when multiplied by 0, gives you 5". But there's no such thing (at least, not in conventional number systems).
