The Awesome Power Of Zero

Brush and floss daily. Have fava beans and a nice Chianti with your liver. One plus one is two. The list goes on and on and we never question the contents. We should. I’ll begin the questioning process by asking is one and one always equal to two? In fact is one actually the same as two? What if I can demonstrate it? Ah, I see the scepticism written all over your face. Well, buckle up, my friend, and follow as I prove that one actually equals two.

(Please don’t run away if you are mathematically challenged or if the word ‘mathematics’ leaves you in a cold sweat. Just come along for the ride.)

Claim

1 = 2

Proof

Let a be any real number and let b refer to the same number so

a = b (equation 1)

Multiply both sides of equation 1 by a so that equation 1 becomes

a² = ab (equation 2)

Subtract b² from both sides of equation 2

a² – b² = ab – b² (equation 3)

Recall from your school days that a² – b² = (a + b)(a – b) and ab – b² = (a – b)b so equation 3 becomes

(a + b)(a – b) = b(a – b) (equation 4)

Divide both sides of equation 4 by a- b

a + b = b (equation 5)

We started this proof by letting a = b so equation 5 reduces to

b + b = b (equation 6)

Now b + b = 2b so equation 6 becomes

2b = b (equation 7)

Divide both sides of equation 7 by b and we are left with

2 = 1

QED

Uh! Oh! Is there something wrong with mathematics?

We use mathematics to engineer cars, bridges and planes among many other things. It all seems to work very well, thank you very much. Obviously the so called “proof” that I outlined above is flawed so, class, as an exercise figure out where the flaw is. I’ll provide the answer next week.

In the meantime take a good, hard look at the liver nestled among the fava beans.

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EDITED: Don’t look at the comments until you figure out the answer. Or already know the answer. Or can’t be bothered working out the answer.