What’s stopping mathematicians from defining a number for 1 ÷ 0, like what they did with √-1?
In: Mathematics
division (a/b) answers the question “suppose I have b*x=a. what is x?” Well if b is 0, x cant be anything, since 0*anything is 0, and a is not 0.
and it is a key property of multiplication that anything*0 **IS** 0 so you cant redefine that property. that just leaves you in an impossible position where the answer to 0*x=a is unanswerable (unless a is also 0). even i*0=0
This brings us to the interesting 0/0, which is undefined. if you look at the equation 0*x=0, x could be ANYTHING and it would be true, so 0/0 is simultaneously ALL numbers.
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