1 divided by 0 is undefined because there is no number that, when multiplied by 0, equals 1.
Explanation
Division can be thought of as the inverse operation of multiplication. When we ask "what is 1 divided by 0?", we are essentially asking "what number, when multiplied by 0, gives us 1?".
Mathematically, we can represent this as:
1 / 0 = x
This is equivalent to:
0 * x = 1
However, any number multiplied by zero always results in zero. Therefore, there is no value for 'x' that satisfies the equation 0 * x = 1.
The Issue with Limits (Advanced Explanation - Optional)
While limits can approach infinity as the denominator approaches zero, this does not define 1/0. For example, the limit of 1/x as x approaches 0 from the positive side is positive infinity, and the limit as x approaches 0 from the negative side is negative infinity. Since the limits from the left and right are not equal, the limit of 1/x as x approaches 0 does not exist. This further demonstrates that division by zero is undefined.
Summary
The fundamental reason 1 divided by 0 is undefined is because it violates the basic rules of arithmetic. Division is the inverse of multiplication, and there is no number that, when multiplied by 0, results in a non-zero number like 1. Anything multiplied by 0 is always 0.
