Really? Well, let's check this out and examine.
0 = 2
Step 1: 0 = (100 - 100) / (100 -100)
Step 2: 0 = (10(*square) - 10(*square)) / ( (10)(10) - (10)(10) )
*means 10 squared - 10 squared
Factoring out numerator through "Difference of 2 Squares" gives us:
Step 3: 0 = ( (10 + 10)(10 - 10)) / ( (10)(10) - (10)(10) )
Step 4: Using the distributive property into the denomator, it gives us:
0 = ( (10 + 10)(10 - 10)) / ( 10 * (10 - 10) )
Step 5: Thus divide out (10 - 10), gives us:
0= ( 10 + 10) / ( 10 )
Step 6: 0 = 20 / 10
Answer: 0 = 2
Haha...As we can see, it seems right. Where is the problem?
The problem is in Step 5, it is invalid since "division by zero" is undefined.
0/0 has no value and is this is called an indeterminate form.
If you carefully examine Step 5, it would turn out that 0 is equal to any number, which is very wrong.
Check this out using another representation of Step 5.
Equation. 1: 0 = (2 * 0) / (1 * 0)
Equation. 2: 0 = (3 * 0) / (5 * 0)
Both equation are correct but if using the invalid process in Step 5, it would be the same as:
Equation. 1: 0 = (2 )(0) / (1)(0)
Divide out 0 in the denominator
0 = 2/1
0 = 2
Equation. 2: 0 = (3)(0) / (5)(0)
Divide out 0 in the denominator
0 = 3/5
Now, we've seen where the problem is. :)
