Analysis:
1. Differentiate it and put into the refrig. Then integrate it in the refrig.
2. Redefine the measure on the referigerator (or the elephant).
3. Apply the Banach-Tarsky theorem.
Number theory:
1. First factorize, second multiply.
2. Use induction. You can always squeeze a bit more in.
Algebra:
1. Step 1. Show that the parts of it can be put into the refrig
“First and above all he was a logician. At least thirty-five years of the half-century or so of his existence had been devoted exclusively to proving that two and two always equal four, except in unusual cases, where they equal three or five, as the case may be.” — Jacques Futrelle, “The Problem of Cell 13″
Most mathematicians are familiar with — or have at
“Psst, c’mere,” said the shifty-eyed man wearing a long black trenchcoat, as he beckoned me off the rainy street into a damp dark alley. I followed.
“What are you selling?” I asked.
“Geometrical algebra drugs.”
“Huh!?”
“Geometry drugs. Ya got your uppers, your downers, your sidewaysers, your inside-outers…”
“Stop right there,” I interrupted. “I’ve never heard of inside-outers.”
“Oh, man
Theorem: 1 = -1
Proof:
1 = sqrt(1) = sqrt(-1 * -1) = sqrt(-1) * sqrt(-1) = 1^ = -1
Also one can disprove the axiom that things equal to the same thing are equal to each other.
1 = sqrt(1)
-1 = sqrt(1)
Therefore 1 = -1
As an alternative method for solving:
Theorem: 1 = -1
Proof:
x=1
x^2=x
x^2-1=x-1
Theorem: 4 = 5
Proof:
-20 = -20
16 – 36 = 25 – 45
4^2 – 9*4 = 5^2 – 9*5
4^2 – 9*4 + 81/4 = 5^2 – 9*5 + 81/4
(4 – 9/2)^2 = (5 – 9/2)^2
4 – 9/2 = 5 – 9/2
4 = 5
Theorem: n=n+1
Proof:
(n+1)^2 = n^2 + 2*n + 1
Bring 2n+1 to the left:
(n+1)^2 – (2n+1) = n^2
Substract n(2n+1) from both sides and factoring, we have:
(n+1)^2 – (n+1)(2n+1) = n^2 – n(2n+1)
Adding 1/4(2n+1)^2 to both sides yields:
(n+1)^2 – (n+1)(2n+1) + 1/4(2n+1)^2 = n^2 – n(2n+1) + 1/4(2n+1)^2
This may be written:
[ (n+1) – 1/2(2n+1)
Theorem: 1$ = 1c.
Proof:
And another that gives you a sense of money disappearing.
1$ = 100c
= (10c)^2
= (0.1$)^2
= 0.01$
= 1c
Here $ means dollars and c means cents. This one is scary in that I have seen PhD’s in math who were unable to see what was wrong with this one. Actually I am crossposting this to sci.physics
Theorem : All numbers are equal to zero.
Proof: Suppose that a=b. Then
a = b
a^2 = ab
a^2 – b^2 = ab – b^2
(a + b)(a – b) = b(a – b)
a + b = b
a = 0
Furthermore if a + b = b, and a = b, then b + b = b, and 2b = b
Theorem: 1 = 1/2:
Proof:
We can re-write the infinite series 1/(1*3) + 1/(3*5) + 1/(5*7) + 1/(7*9)
+…
as 1/2((1/1 – 1/3) + (1/3 – 1/5) + (1/5 – 1/7) + (1/7 – 1/9) + … ).
All terms after 1/1 cancel, so that the sum is 1/2.
We can also re-write the series as (1/1 – 2/3) + (2/3 – 3/5)
Theorem: log(-1) = 0
Proof:
a. log[(-1)^2] = 2 * log(-1)
On the other hand:
b. log[(-1)^2] = log(1) = 0
Combining a) and b) gives:
2* log(-1) = 0
Divide both sides by 2:
log(-1) = 0… More...