It is undefined because the inverse of division is multiplication. If you multiply by zero, every answer is zero. If you try to invert that operation you can’t know which number was multiplied by zero to get zero because multiplying by zero doesn’t produce a unique answer for each operation.
Additionally, if you take the limit of 1/x as x approaches zero from the positive side the result approaches positive infinity. If you take the limit from the negative side it approaches negative infinity.
It is undefined because the inverse of division is multiplication. If you multiply by zero, every answer is zero. If you try to invert that operation you can’t know which number was multiplied by zero to get zero because multiplying by zero doesn’t produce a unique answer for each operation.
Additionally, if you take the limit of 1/x as x approaches zero from the positive side the result approaches positive infinity. If you take the limit from the negative side it approaches negative infinity.