Calculus Problem
Calculus Problem
(OP)
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.
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






RE: Calculus Problem
RE: Calculus Problem
RE: Calculus Problem
http://en.wikipedia.org/wiki/Invalid_proof
RE: Calculus Problem
RE: Calculus Problem
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.
RE: Calculus Problem
RE: Calculus Problem
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.
RE: Calculus Problem
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