-1 / 0 can be defined to be a special new number, ⭐.
This system of numbers is actually mathematically consistent and has all the properties that a number system should have. But using simple algebra, you can prove that in this new number system, ⭐ = 0. And then you can also prove that all other numbers equal zero.
This number system is known as the zero ring, and it’s the ring where the only number is 0 and the following operations are defined:
0 + 0 = 0
0 - 0 = 0
0 × 0 = 0
0 ÷ 0 = 0
0^0 = 0
All other symbols, including 1, 2, and ⭐, are just alternative labels for 0 in this number system. In other words, defining division by zero is essentially the equivalent of reality collapsing in mathematics.
So yes, you can validly define division by zero. You just get degenerate mathematics if you do. So be careful what you wish for.
-1 / 0 can be defined to be a special new number, ⭐.
This system of numbers is actually mathematically consistent and has all the properties that a number system should have. But using simple algebra, you can prove that in this new number system, ⭐ = 0. And then you can also prove that all other numbers equal zero.
This number system is known as the zero ring, and it’s the ring where the only number is 0 and the following operations are defined:
All other symbols, including 1, 2, and ⭐, are just alternative labels for 0 in this number system. In other words, defining division by zero is essentially the equivalent of reality collapsing in mathematics.
So yes, you can validly define division by zero. You just get degenerate mathematics if you do. So be careful what you wish for.
This would have been so much easier to understand in school. Why aren’t we using this instead!?