May 11

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.

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.

Category: Mathematics | 5 Comments on The Awesome Power Of Zero
April 1

Everything You Added Was Wrong

For thousands of years we have tacitly assumed that 1 + 4 = 5. This is a false assumption says April Schlemiel, head of the Department of Mathematics at Caper University, California. Professor Schlemiel argues that numbers obey laws that are actually quite different to what we have always used. She likens these laws to the Laws of Relativity.

“Relativity turned Physics on its head,” she said, “by showing that space and time are intricately linked with the matter it contains; the matter in the Universe curves space-time which in turn influences the motion of matter. In a similar way numbers and the operations on numbers are intricately linked; addition, for example, curves the number continuum while numbers influence the operation itself. In other words 1 + 4 is not exactly 5.”

In a paper presented at the International Mathematical Symposium, Professor Schlemiel offered proof for her revolutionary theorem, The Relativity of Numbers. It was the mathematical equivalent of a blockbuster movie. While a few present adopted a “wait and see” stance, April Schlemiel won the support and acclaim of the world’s best mathematical minds.

“It makes sense if you think about it,” says Unas Quatro, Professor of Advanced Mathematics at Lackey University, London. “Throughout history we’ve seen mathematics used to elaborate the theories of physics which in turn creates new mathematics to deal with the new ideas. I won’t be surprised if we soon see a quantum theory of numbers as well.”

So what does this mean for the rest of us average citizens? Not to worry, says Professor Schlemiel.

“Relativity applies at speeds approaching the speed of light. In the same way the Relativity of Numbers is only significant in the large number domain under complex operations. We can go on adding 1 to 4 and continue using 5 as the answer because it is 5 to all intensive purposes.”

After a slight pause she grinned slyly and added that perhaps we should worry after all since the national debt is rapidly approaching the relativistic domain.

Category: Mathematics, Physics, Science | 3 Comments on Everything You Added Was Wrong