# Strange Mathematics

#### Dave

Joined Nov 17, 2003
6,970
you have divided both sides by x-y=0.division by zero is "illegal".why?
consider p/0 = q; p and q are non-zero.
we have p=0*q.say p=10
no value of q when multiplied with 0 will give you 10.
please comment,if you feel that there are faults with my posts or if i can improve my explanations...thank you
The solution of a/0 is undefined (it has real no meaning): http://en.wikipedia.org/wiki/Division_by_zero

Dave

Joined May 1, 2007
19
hello dave

the reason why xz=yz implies x=y for z<>0 is that such z has a multiplicative inverse: multiplying both sides of the equation by 1/z gives the required conclusion. zero has no multiplicative inverse: if w is supposed to be a multiplicative inverse of zero then by definition w(0)=1, contradicting the fact that x(0)=0 for all x.

hope that helps

peace
stm

#### kautilya

Joined Apr 26, 2007
39
Here's one:

Say: x = y

Then: x - y = 0

And: 2x - 2y = 0

So: x - y = 2x - 2y

Taking common factors: 1(x - y) = 2(x - y)

Therefore: 1 = 2 !!!

(I know this is not really the answer, but it certainly confuses many who see it!)

Dave
This question may be hilarious but it violates the very essence of mathematics. As rightly pointed out, division by zero is not permitted.

#### Dave

Joined Nov 17, 2003
6,970
This question may be hilarious but it violates the very essence of mathematics. As rightly pointed out, division by zero is not permitted.
But to the casual mathematician the sequence of steps to the result is wholly intuitive and correct. I suppose the message from this exercise is to verify any assumptions you make; for example when you state x - y = 2x - 2y ask yourself, what does that imply?

All subsequent steps from x - y = 2x - 2y are standard maths procedures, however the user is tricked into not realising that since x = y, x - y = 2x - 2y = 0.

Dave