Why can’t you invent an imaginary number for division by zero like you can for a square root of a negative?
In: Mathematics
Using imaginary numbers for the square root of a negative number gives something useful. It may not be within the Real number spectrum, but it definitely is a value that exists.
Division by zero does not exist.
Division at its base concept is to take a group and split it into a specific number parts.
Take 10 marbles divided by 5. The result is 5 groups of 2.
It’s the opposite of multiplication. One handy tool I learned when younger is that when imagining multiplication with physical objects, the word “of” often means “multiply”.
Notice: 5 groups **of** 2 is a total of 10. 5 x 2 = 10.
By definition, division needs to be a reversible process.
Imagine dividing 10 by 4 now. You’d need to split it into 4 groups of 2.5.
Into 3, and you’d need 3 groups of 3.333…
Into 2, 2 groups of 5.
Divide by 1, and a single group of 10.
Each of these is reversible multiply each and you’ll get back to 10.
Divide by 0, and how many groups do you split 10 into?
It’s just not a thing.
What about the reverse? 0 times X = 10. X could be anything. It’s not a reversible process with a definitive answer. You could make it anything, and if it can be anything, then dividing by zero cannot be defined.
If you want an example for how dividing by zero breaks everything, [watch this math teacher prove that 1 = 2](https://www.youtube.com/watch?v=hI9CaQD7P6I).
See if you can identify the step where the proof breaks. Hint, there’s a point where he ends up dividing by zero. He just masks it by using variables.
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