Hi one of my friend showed me one proof i.e.
$1)$ $2^2 - 2^2 = 10 - 10$
$2)$ $(2+2) (2-2) = 5 (2-2)$
$3)$ dividing both sides by (2-2)
$4)$ $(2 + 2) = 5$
I know this is wrong in first line as both LHS and RHS goes to 0 and u can't directly make a equation 0=0
because 0/0 != 1
but i can't explain this can anyone give a perfect reason why can't we compare 0=0
or is there any other reason also for this to be wrong?????
Answer
You can't divide both sides by $(2-2)$, because $(2-2)$ is zero, and you cannot divide by zero.
The technical reason for this is that zero does not have a multiplicative inverse in the field of rational numbers (or real numbers, or complex numbers, or any field), because the existence of such an inverse would be inconsistent with the field axioms.
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