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Weight of an Elephant

Show that the weight of a mouse is equal to the weight of an elephant.

See if you can find the fault in the following proof.

Let the weight of an elephant be E

Let the weight of a mouse be M

Let the average (mean) weight of a mouse and elephant be W

Then E + M = 2W

Rearranging;

E = -M + 2W (i)

and E – 2W = -M (ii)

multiplying; E(E – 2W) = -M(-M + 2W)

E² – 2EW = M² – 2MW

Add W² to both sides

E² – 2EW + W² = M² -2MW + W²

(E - W)² = (M - W)²

Take the square root of both sides

E - W = M - W

Add W to both sides

E = M i.e. the weight of an elephant is equal to the weight of a mouse

What is the problem?

Remember that the square root of a number has both the positive and negative value

e.g. = 2 i.e. 2 or -2.

Similarly = + (E + W) or –(E + W)

i.e. E + W or –E –W

By only taking the positive value we eliminate half the answer and can prove (erroneously) that a mouse weighs as much as an elephant.