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 because I think that the latter makes a very nice introduction to the importance of keeping track of your dimensions.
Theorem: 3=4
Proof:
Suppose:
a + b = c
This can also be written as:
4a - 3a + 4b - 3b = 4c - 3c
After reorganizing:
4a + 4b - 4c = 3a + 3b - 3c
Take the constants out of the brackets:
4 * (a+b-c) = 3 * (a+b-c)
Remove the same term left and right:
4 = 3
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, which mean that 2 = 1.
Theorem: All positive integers are equal.
Proof: Sufficient to show that for any two positive integers, A and B, A = B.
Further, it is sufficient to show that for all N > 0, if A and B (positive integers) satisfy (MAX(A, B) = N) then A = B.
Proceed by induction.
If N = 1, then A and B, being positive integers, must both be 1. So A = B.
Assume that the theorem is true for some value k. Take A and B with MAX(A, B) = k+1. Then MAX((A-1), (B-1)) = k. And hence (A-1) = (B-1). Consequently, A = B.
When should you stop for a glow worm?
→ When he has a red light!
What did the worm say to the other when he was late home?
→ Where in earth have you been!
How do you make a glow worm happy?
→ Cut off his tail, he'll be de-lighted!
How can you tell which end of a worm is which?
→ Tickle it in the middle and see which end laughs!
How can you tell if you are looking at a police glow worm?
→ It has a blue light!
Who is the worm's Prime Minister?
→ Maggot Thatcher!
