Zero-infinity hypothesis

Question

math.stackexchange community. I have joined to inquire on a hypothesis a friend of mine has recently proposed. Please note: before posting this, I have repetitively told him that his logic is flawed in a plethora of ways. But I'll humor him, just this once.

This dear friend of mine claims that when [sic] divided by zero, infinity equals all real numbers, or as follows: ∞ / 0 = (-∞, ∞)

Oh, my fellow mathematicians and logicians, please inform my friend of either his grave error or his genius discovery. Thank you.

Answer 1

Your friends claim is precluded by the fact that nothing can be divided by zero. It all goes back to having 5 cookies and dividing them up into zero groups. You can't tell how many cookies are in each group. The fact that it is infinity being divided has nothing to do with it.