The logical problem
You can’t divide by zero because there’s no number you can multiply by 0 to get a non-zero result. If a÷0=xa\div 0 = xa÷0=x then 0⋅x=a0\cdot x = a0⋅x=a. But 0⋅x=00\cdot x = 00⋅x=0 for every xxx. So unless a=0a=0a=0, no such xxx exists — the operation is undefined.
Infinity isn’t a number
People sometimes say “let x=∞x=\inftyx=∞,” but infinity isn’t a normal number like 5 or −2. As you divide by smaller and smaller numbers (1, 0.1, 0.01…), the quotient grows without bound; the limit can be “infinite,” but at exactly zero the expression has no well-defined value.
What about black holes?
Physics throws up singularities — places where our equations predict “infinite density.” That’s a signal the math (general relativity) has broken down there. Physicists expect a better theory (quantum gravity) will replace that breakdown, not that division-by-zero suddenly becomes legal.
Cookie rule
Dividing by zero is like trying to divide cookies among zero people: the question itself makes no sense. Try it on a calculator — you’ll get “UNDEFINED” or an error.