You are undersimplifying. What you are actually implying in the lkast strep is dividing both sides by (a^2-ab). Unfortunately given that a=b then you are actually attempting to divide by zero which is not ion I am afraid!
Yep! - Sorry!. Sorry too for my atrocious spelling above - probably been drinking! Having said all that we had this out with a Maths teacher when I was doing A and AS maths - he posed it as a potential proof and we (including a current Prof at StAndrews ex Oxford) still failed to spot the problem for a time. It is one of those good training exercises for examining what you actually MEAN when you 'factorise' and 'simplify'.
You know that you can't arbitrarily cut off the rest of it!
ReplyDelete
ReplyDeleteLet a = b
a^2 = ab
a^2 +a^2 = a^2 + ab
By subtracting 2ab from both sides we get:
2a^2 - 2ab = a^2 - ab
Then we can factorize to get:
2(a^2 - ab) = a^2 - ab
Which simplifies to: 2=1
//Which simplifies to: 2=1//
ReplyDeleteYou are undersimplifying. What you are actually implying in the lkast strep is dividing both sides by (a^2-ab). Unfortunately given that a=b then you are actually attempting to divide by zero which is not ion I am afraid!
It's all the little technicalities with you, isn't it?
ReplyDeleteYep! - Sorry!. Sorry too for my atrocious spelling above - probably been drinking!
ReplyDeleteHaving said all that we had this out with a Maths teacher when I was doing A and AS maths - he posed it as a potential proof and we (including a current Prof at StAndrews ex Oxford) still failed to spot the problem for a time.
It is one of those good training exercises for examining what you actually MEAN when you 'factorise' and 'simplify'.
Reading the above it appears that I CAN type!
http://www.milkandcookies.com/link/296862/detail/
ReplyDeletehttp://www.fark.com/comments/7023252/-6212-9-no-no-6212-1-no-no-6212-2?cpp=1
ReplyDeleteThat Milk and cookies link actually disproves the premise at every step as opposed to proving it!
ReplyDeleteRhapsody on the Proof of Pi = 4
ReplyDeleteShe lost that when she cut the square with a perimieter = 4.
ReplyDeleteDiferent function but still I love her showsQ.