I need some help in this trick equation: E = b + w?

Question

A guy tries to prove that an Elephant and a bird both weigh the same (i.e E = b).
He offers this equation: E= b + w (where w=any extra weight needed to equate the Elephant's).
Now follow this:
E(E-b) = (b + w) (E - b) - multiplying both sides by (E - b).
i.e E2 - Eb = bE + wE - b2 - wb - opening the brackets
or E2 - Eb - wE = bE -b2 -wb - subtrcting wE from both sides
Follow? Now factorise and you have:
E(E - b - w) = b (E - b -w) or E=b
This therefore (according to him) shows that E = b.
Can anybody pls show me the trick (or flaw) of this algebra?

Answer 1

there is a dividing by 0 step, if E=b+w then (E-b-w)=0 so the last part E(E-b-w)=b(E-b-w), simply says 0E=0b. it doesnt follow from there that E=b does it!

Answer 2

e-b-w=0 and division by 0 is indetermined
catch this one
x=x
therefore, x²=x² (squaring both sides)
therefore,x²-x²=x²-x² (subtracting x from both sides)
therefore,x(x-x)=(x-x)(x+x) (taking x common from
first side and apllying
a²-b²=(a-b)(a+b) in
second side)
therefore, x=x+x
therefore x=2x
therefore, 1=2

and this one too
Let A = B. Then A^2 = AB.
A^2 - B^2 = AB - B^2
(A + B)(A - B) = B(A - B)
A + B = B
B + B = B
2B = B
2 = 1

Answer 3

E(E - b - w) = b (E - b -w) is ok
but since w is E-b by definition, E-b-w is zero
so this only says 0=0.
you can't cancel the 0 and apply any meaning to the remainder.

e.g. 1*0 = 10 * 0 does not imply 1 = 10

Answer 4

E= b + w

E - b -w = 0

The trick is that you have divided both sides by 0, which is not allowed.


To paducah_billy: Thanks!

To Daredevil: Division of 0 is indetermined only when the numerator and denominator are both 0.

Answer 5

Give Math Freek 5 stars, he is the man.

Way to go Math Man, the system would not let me give him a thumb up but he deserves one. When you divide by 0, you will get screw up results every time. Good call man.

Answer 6

Notice that in the last expression :
E(E - b - w) = b (E - b -w)
E - b - w = 0 as you initially declared E= b+w
so you cant divide by 0 to recieve E=b;

Answer 7

it particularly is a approach in fixing a differential equation... by some ability physics makes use of it. yet physics isn't the biggest reason or the source. it particularly is by using fact mathematicians relatively involved interior the sphere of differential equations word this. it particularly is barely one attitude in coping with a differential equation. ©

Answer 8

The flaw happens when you divide both sides by E - b - w. That is zero.

Answer 9

Birds weigh the same as elephants...when you divide by zero!

Answer 10

If E = b + w, the n E-b-w = 0
So in the penultimate step, you are dividing by zero which is not allowed.