Here is the equation:
I was very bored today, and messed around with my calculator until I found this. Completely uninteresting huh ?Code:high * high - high = low * low + low where high and low are any real number, and high = low + 1
Here is the equation:
I was very bored today, and messed around with my calculator until I found this. Completely uninteresting huh ?Code:high * high - high = low * low + low where high and low are any real number, and high = low + 1
Do not make direct eye contact with me.
Proof:
YupCode:Given: x = y + 1. Now, prove that x^2 - x = y^2 + y. First, square both sides: x^2 = (y + 1)^2 Expand: x^2 = y^2 + 2y + 1 Subtract x from both sides: x^2 - x = y^2 + 2y + 1 - x We were given that x = y + 1, so substitute on the right side of the equation: x^2 - x = y^2 + 2y + 1 - (y + 1) Simplify: x^2 - x = y^2 + y
FAQ
"The computer programmer is a creator of universes for which he alone is responsible. Universes of virtually unlimited complexity can be created in the form of computer programs." -- Joseph Weizenbaum.
"If you cannot grok the overall structure of a program while taking a shower, you are not ready to code it." -- Richard Pattis.
Well at least its one of the first equations that wasn't burned to the ground on these forums .
Do not make direct eye contact with me.
And now because I'm taking a course called Techniques of Math Proof, here's another proof. This one uses case analysis:
Yeah, I dig proofs.Code:x^2 - x ?= y^2 + y Factor: x (x - 1) ?= y (y+1) Substitute: x (x - 1) ?= xy Case 1: x != 0 Divide both sides by x: x - 1 ?= y Add 1 to both sides: x = y + 1 Case 2: x = 0 Given that x = y + 1 and x = 0, y = -1. x^2 - x ?= y^2 + y Now, just plug in x = 0 and y = -1: 0 = (-1)^2 + -1 0 = 1-1
FAQ
"The computer programmer is a creator of universes for which he alone is responsible. Universes of virtually unlimited complexity can be created in the form of computer programs." -- Joseph Weizenbaum.
"If you cannot grok the overall structure of a program while taking a shower, you are not ready to code it." -- Richard Pattis.
Well, there are now two proofs supporting your conjecture, so one can't argue with the truth. It still remains useless as you said.Originally posted by Lurker
Well at least its one of the first equations that wasn't burned to the ground on these forums .
FAQ
"The computer programmer is a creator of universes for which he alone is responsible. Universes of virtually unlimited complexity can be created in the form of computer programs." -- Joseph Weizenbaum.
"If you cannot grok the overall structure of a program while taking a shower, you are not ready to code it." -- Richard Pattis.
For any x, y and a, where they are all elements of R, and y = x - a, x^2 - ax = y^2 + ay.
Code:x^2 - ax = (x - a)^2 + a(x-a) x^2 - ax = x^2 - 2ax + a^2 - a^2 + ax x^2 - ax = x^2 - ax
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a lot of discoveries in the world of mathematics are useless, so don't feel too bad.
look at it this way: you can use it as a really long way to find out if there are two consecutive numbers... or to prove that high-low=1, if high is low+1 and they're both real numbers
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Originally posted by major_small
look at it this way: you can use it as a really long way to find out if there are two consecutive numbers... or to prove that high-low=1, if high is low+1 and they're both real numbers
Do not make direct eye contact with me.