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
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
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 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, you'll love 'em. Makes you feel like M.C. ever-lovin' Escher on a particularly weird day."
"Go on..."
"OK, your inside-outers, your arbitrary bilinear mappers, and here, heh, here are the best ones," he said, pulling out a large clear bottle of orange pills.
"What are those, then?" I asked.
"Givens transformers. They'll rotate you about more planes than you even knew existed."
"Sounds gross. What about those bilinear mappers?"
"There's a whole variety of them. Here's one you'll love -- they call it 'One Over Z' on the street. Take one of these little bad boys and you'll be on speaking terms with the Point at Infinity."
"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, you'll love 'em. Makes you feel like M.C. ever-lovin' Escher on a particularly weird day."
"Go on..."
"OK, your inside-outers, your arbitrary bilinear mappers, and here, heh, here are the best ones," he said, pulling out a large clear bottle of orange pills.
"What are those, then?" I asked.
"Givens transformers. They'll rotate you about more planes than you even knew existed."
"Sounds gross. What about those bilinear mappers?"
"There's a whole variety of them. Here's one you'll love -- they call it 'One Over Z' on the street. Take one of these little bad boys and you'll be on speaking terms with the Point at Infinity."
misunderstood people
1. They speak only the Greek language.
2. They usually have long threatening names such as Bonferonni, Tchebycheff, Schatzoff, Hotelling, and Godambe. Where are the statisticians with names such as Smith, Brown, or Johnson?
3. They are fond of all snakes and typically own as a pet a large South American snake called an ANOCOVA.
4. For perverse reasons, rather than view a matrix right side up they prefer to invert it.
5. Rather than moonlighting by holding Amway parties they earn a few extra bucks by holding pocket-protector parties.
6. They are frequently seen in their back yards on clear nights gazing through powerful amateur telescopes looking for distant star constellations called ANOVA's.
7. They are 99% confident that sleep can not be induced in an introductory statistics class by lecturing on z-scores.
8. Their idea of a scenic and exotic trip is traveling three standard deviations above the mean in a normal distribution.
9. They manifest many psychological disorders because as young statisticians many of their statistical hypotheses were rejected.
10. They express a deap-seated fear that society will someday construct tests that will enable everyone to make the same score. Without variation or individual differences the field of statistics has no real function and a statistician becomes a penniless ward of the state.
2. They usually have long threatening names such as Bonferonni, Tchebycheff, Schatzoff, Hotelling, and Godambe. Where are the statisticians with names such as Smith, Brown, or Johnson?
3. They are fond of all snakes and typically own as a pet a large South American snake called an ANOCOVA.
4. For perverse reasons, rather than view a matrix right side up they prefer to invert it.
5. Rather than moonlighting by holding Amway parties they earn a few extra bucks by holding pocket-protector parties.
6. They are frequently seen in their back yards on clear nights gazing through powerful amateur telescopes looking for distant star constellations called ANOVA's.
7. They are 99% confident that sleep can not be induced in an introductory statistics class by lecturing on z-scores.
8. Their idea of a scenic and exotic trip is traveling three standard deviations above the mean in a normal distribution.
9. They manifest many psychological disorders because as young statisticians many of their statistical hypotheses were rejected.
10. They express a deap-seated fear that society will someday construct tests that will enable everyone to make the same score. Without variation or individual differences the field of statistics has no real function and a statistician becomes a penniless ward of the state.
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)
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) ]^2 = [ n - 1/2(2n+1) ]^2
Taking the square roots of both sides:
(n+1) - 1/2(2n+1) = n - 1/2(2n+1)
Add 1/2(2n+1) to both sides:
n+1 = n
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) ]^2 = [ n - 1/2(2n+1) ]^2
Taking the square roots of both sides:
(n+1) - 1/2(2n+1) = n - 1/2(2n+1)
Add 1/2(2n+1) to both sides:
n+1 = n
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