mathematically, how to prove we cant divide by zero. and why multiplication of zero with any number leads to zero itself . can we mathematically prove that

Answer 1

I can prove it logically.

If a cake sits on the table and no one (0) eat it, the cake is still whole.

If you have $100.00 saved and it doesn't earn interest, it's multiplied by 0 and doesn't change.

Answer 2

Look at these cases:

12/3 = 4 because 3x4 = 12
20/10 = 2 because 2x10 = 20
5/0 = ?? because ?? x 0 = 5 , but that is a contradiction, since anything times zero is zero.

or

5/.1 = 50
5/.01 = 500
5/.001 = 5000
5/.000000000001 = 5000000000000
notice I am dividing by a smaller and smaller number and my answer is getting bigger and bigger, or "bigly" as Trump would say.

so as the divisor is getting closer and closer to zero, my answer is approaching infinity.
But mathematically we consider such an infinitely large number as "undefined"

Answer 3

here is another explanation:
if multiplication is repeated addition,
e.g. 3x4 = 3+3+3+3 = 12
and division is repeated subtraction:
e.g.
20 ÷ 4

20-4 = 16
16-4 = 12
12-4 = 8
8-4 = 4
4-4 = 0
I subtracted the 4 five times to get to zero
so 20÷4 = 5

so how about 20 ÷ 0
20-0 = 20
20-0 = 20
20-0 = 20
...
how many times would I have to subtract the zero to get to zero ???

Answer 4

As long as we're dividing by zero, what about 0/0? Why is it undefined?

Suppose there is a value x such that

0/0 = x
Then, multiplying by zero, we get
0 = 0*x
But that is true for any value of x. So there is no particular value we can say is equal to 0/0.

Answer 5

I always taught that 0/0 was indeterminate and did not fall into the "undefined" category.

Such as in limits that result in 0/0 situations,
e.g.
lim (x^2 - 4)/(x-2) , as x ---> 2
you would get 0/0

= lim (x-2)(x+2)/(x-2) as x ---> 2
= limi x+2 , as x --->2
= 4
so in this case 0/0 yields a result of 4

But Steve knows all that , I am sure.