Dividing by Zero

[The Student]

Is the reason why we can't divide by zero because if x = 0, the x^(-1)*0 ≠ 1, using the inverse identity as the axiom?

 

[tkhunny]

Maybe, but I like the 2nd Grade Explanation.

6/2 = 3 Why? Because 3 twos is 10.

10/5 = 2 Why? Because 2 fives is 10

15/0 is NaN Why? Because how many 0s are required to make 15?

 

[lookagain]

Maybe, but I like the 2nd Grade Explanation.

6/2 = 3 Why? Because 3 twos is 10.

10/5 = 2 Why? Because 2 fives is 10

15/0 is NaN Why? Because how many 0s are required to make 15?

0/0 is indeterminate. Why? Because how many 0s are required to make 0?

 

[HallsofIvy]

Is the reason why we can't divide by zero because if x = 0, the x^(-1)*0 ≠ 1, using the inverse identity as the axiom?

Yes. Dividing by "x" is the same multiplying by \(\displaystyle x^{-1}\) which must have the property that \(\displaystyle x^{-1}(x)= 1\) and there simply is no number, y, such that y*0= 1.