| #1965 The birthday study It is proven that the celebration of birthdays is healthy. Statistics show that those people who celebrate the most birthdays become the oldest. -- S. den Hartog, Ph D. Thesis Universtity of Groningen... |
| #1964 Story about infinity A very large mathematical convention was held in Las Vegas. The conventioneers filled two hotels, each with an infinite number of rooms. The hotels were across the street from each other and were owne... |
| #1963 Two plus two is five "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 unus... |
| #1962 Math is turning bad "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... |
| #1961 Four is equal to five 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
... |
| #1960 N equals N plus one 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)... |
| #1958 Numbers equal zero 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, th... |
| #1957 One equal to one half 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... |
| #1956 Log negative one zero 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
... |
| #1955 All numbers are equal Theorem: All numbers are equal.
Proof: Choose arbitrary a and b, and let t = a + b. Then
a + b = t
(a + b)(a - b) = t(a - b)
a^2 - b^2 = ta - tb
a^2 - ta = b^2 - tb
a^2 - ta + (t^2)/4 = b^2 - ... |
| #1954 One plus one are two Theorem: 1 + 1 = 2
Proof:
n(2n - 2) = n(2n - 2)
n(2n - 2) - n(2n - 2) = 0
(n - n)(2n - 2) = 0
2n(n - n) - 2(n - n) = 0
2n - 2 = 0
2n = 2
n + n = 2
or setting n = 1
1 + 1 = 2
... |
| #1953 Dollars equal ten cents Theorem: 1$ = 10 cent
Proof:
We know that $1 = 100 cents
Divide both sides by 100
$ 1/100 = 100/100 cents
=> $ 1/100 = 1 cent
Take square root both side
=> squr($1/100) = squr (1 cent)
=> $ 1/... |
| #1952 Three is equal to four 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:
... |
| #1951 Equal positive integers 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... |