Calculus Problem 3

[msquared48]

OK guys, my grandaughter is taking calculus this year, and I remember a problem from second quarter Freshman calculus where there was a "proof" of 1 + 1 = 3 and we had to find what was wrong with it. After 40+ years, I no longer have my notes, and was wondering if this jogs anyone's memory.

Does anyone remember the "proof" and what was wrong with it? This is not a joke. Thanks in advance for all responses.

Mike McCann
McCann Engineering

 

[gwynn]

The one I vaguely remember contains division by zero. Don't remember the proof though.

 

[quark]

Just check whether the function is discontinuous in the applied range.

 

[Tomfh]

You might find it in here:

http://en.wikipedia.org/wiki/Invalid_proof

 

[msucog]

it hasn't been nearly as long for me and i still don't recall the exact procedure. i believe quark is probably correct. i do remember the problem but calculus was far from my strong point...all the many times i retook it. thank god my pay is based on my performance and not on my college GPA (at least i did well in my civil class...most of them anyway).

 

[Dinosaur]

I believe the proof you are thinking of begins with a + b = 1. Later in the proof the variables a = b = 1 are established. And the result, a + b = 1 then becomes the confusion. In this proof, there is a step where they divide by 0, but you have to recognize it because it is expressed as a step where the formula says something like (a - b) x a = something else. Later they cancel the (a - b) term from both sides of the equals sign. At this point they divided by (a - b) which is zero.

The proof I enjoy more ends up with "women = evil". Ever hear of that one?

To have a woman you have to expect to spend time and money ...

Women = time x money

But we all know that time is money ...

Time = money

Which may be substituted into our original equation to obtain ...

Women = Money x (Money)

which simplifies to ...

Women = (Money)^2

We also know that money is the root of all evil, which may be expressed mathmatically as ...

Money = SQRT(evil)

and we then obtain by substitution ...

Women = (SQRT(evil))^2

And we may simplify this to ...

Women = Evil

Maybe your grandfather would enjoy that proof.

 

[JStephen]

I may have this in one of my Martin Gardiner books- will check when I get home. Seems like they factor out a term which is actually zero. Of course, there's bound to be lots of ways to work the details.

 

[JStephen]

Proof that any number A is equal to a smaller number B:
Let A = B + C
Multiply both sides by (A-B) to get
A^2 - AB = AB + AC -B^2-BC
Move AC to the left side:
A^2 - AB - AC = AB -B^2 - BC
Factor:
A(A-B-C) = B(A-B-C)
Divide each side by A-B-C to get:
A = B

Note that from the definition, A-B-C = 0, so that last step divides each side by zero.

This is from P. 143 of "Hexaflexagons and Other Mathematical Diversions" by Martin Gardner.

 

[dik]

a = b
a a = a b
a^2 = a b
a^2 - b^2 = a b - b^2
(a + b)(a - b) = b (a - b)
(a + b) = b
Since a = b
(a + a) = a
2 a = a
2 = 1