Why can’t you invent an imaginary number for division by zero like you can for a square root of a negative?
In: Mathematics
My favorite explanation for this is the t shirt dilemma. Say you have $100 and t shirts cost $5. Then you can buy 100/5=20 t shirts. But what if t shirts are free? You could buy 1, or 10, or 50, or literally any number of shirts. So we say that 100/0 is “undefined” because there are multiple possible correct answers. It’s not that we can’t invent something to represent the value of 100/0, it’s that there is no single correct such value.
As others have said, you can also see this algebraically using an equation. But that’s not appropriate for most five year olds.
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