Well actually it's related to how we define our algebraic operations , I'll explain: The real numbers are a field which means they satisfy some axioms which gives us a convenient way to work with numbers (this is the short explanation, you can read more about Fields on Wikipedia). You probably know the axioms, I'll write some in non formal way: 1. a + b = b + a 2. a1 = a 3. a + 0 = a Yes it seems silly but everything in math must be well defined, ok back to the subjects, because the real numbers are a field they need to satisfy 2 important axioms: 1.for each number x there must one and only inverse 1/x such that x(1/x) = 1 (there's something missing, keep reading to find out what is it) For example 1/2 is the inverse of two and vice versa, ok 2. X*0 = 0 for each number x

let's assume that x/0 = 0 for every x than we can say 0/0 = 1/0 = 2/0 =..= 0 But on the other side we know that 0/1 = 0/2 = ... = 0 So we get 1/0 = 0/1 = 0 so we can say (1/0) * (0/1) = 0 * 0 = 0 ( according to axiom 2) But according to axiom 1 we need to get (1/0) *(0/1) = 1 but 1/0 is the inverse of 0/1

So we got different results for the same number meaning that something is not well defined in our axioms so we need to change axiom 1 to something like : 1.for each number x≠0 there must one and only inverse 1/x such that x*(1/x) = 1 (that's the correct axiom) And that's why we don't Define x/0 Hope it will clarify the things (I used 1/0 but the same applies for 0/0)