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1=0
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Posted by: Ghetto Blasta
So I'm reading this book called "Zero". Naturally, it's a book all about 0. It's origins, properties, ect. It was pretty straight forward untill I got to page 23, where it lists a reference to Appendix A in which it claims it proves Winston Churchill is a carrot. Being the curious individual that I am, I wanted to know how in hell they could prove that Winston Churchill is a carrot. It begins with the algebra problem as follows:
Let a and b = 1. Since a and be are equal,
b^2 = ab (eq. 1)
Since a=a,
a^2 = a^2 (eq. 2)
subtract equation 1 from equation 2, and we get
a^2-b^2 = a^2-ab (eq. 3)
Factor both sides of the equation.
(a-b)(a+b) = a(a-b) (eq. 4)
Divide both sides by (a-b)
a+b=a (eq. 5)
Subtract a from both sides
b = 0 (eq. 6)
Since b = 1
1 = 0 (eq. 7)
............WhAT?! This is where logic, as we know it, was torn into tiny bits of confetti. Everyone knows 1 = 1. 1 sofa = 1 sofa. how can 1 sofa = no sofas?
But it doesn't stop there. Oh no. It goes on to prove more crazyness.
Winston Churchill has 1 head, but if 1 = 0, then he has 0 heads. Likewise, if Churchill has no leafy tops, then because 1 = 0, he has a leafy top.
Multiply both sides of the equation by 2
2 = 0 Winiston has 2 arms, and 2 legs, but if 2 = 0, then Winston has 0 arms and 0 legs.
If you multiply both sides of equation 7 by Churchills waist size
(Churchill's waist size) = 0
Therefore, Churchill has no waist size and tapers to a point.
Next, we multiply equation 7 by the wavelengths of all the different photons coming out of him.
(Churchill's photon's wavelength) = 0
If we then multiply equation 7 by 640 nanometers (wavelength for the color orange)
640 = 0
Therefore, any photon that comes out of Winston is orange.
Add all that together, and they just proved, mathematically, that Winston Churchill is a carrot. Now look in the mirror and tell me your eyes aren't doing this:  
Posted by: AK47
Posted by: Gunslinger
I've seen that conjecture posted on a forum somewhere before. It's pretty much....well....flawed.
The only thing they proved mathematically is that they think it is permissable to divide by zero and that 1+1=1.
Posted by: Ghetto Blasta
yeah they go on to show the flaw in the next paragraph, but I just thought it was an interesting anomoly type thing.
What's REALLY confusing, is the Babylonian counting system. It's base-60 and only had 2 symbols for a long time, until they added a 3rd.
Posted by: Gunslinger
Oh.
Well, as long as nobody starts screaming that the repeating decimal .9999 is equal to 1, then all will be good, and the moderators will stay happy.
Posted by: Null Actor
Dividing by zero is basic calculus - you end up with infinity.
Zero, however, is a hack.
Posted by: Ghetto Blasta
See, I havn't taken Calculus yet. That be next year. So I don't know all that fancy shtuff.
Gun, why people seem to think .99999.... equals 1 is beyond me. I mean, you can make it equal to 1, but that's no different that 1=0.
Posted by: Kdr Kane
This thread might be interesting if you had decided to post the flaw "in the next paragraph".
The flaw I see is that you can't divide by zero as was done in Equation 5. That's always undefined.
Posted by: SKYHN
Omg, I remember that insane thing on the bnet forums a long time ago about .99999 = 1. That argument was so funny, people would get tottaly angry over someone else giving their answer to it.
Posted by: Amall
1.9999999999999999 = 2
Posted by: Lord_Buttplug
If I remember correctly, dividing by zero gets you an undefined result. The limit though would head towards infinity.
Posted by: Ghetto Blasta
 Quote:
Originally posted by Kdr Kane
This thread might be interesting if you had decided to post the flaw "in the next paragraph".
The flaw I see is that you can't divide by zero as was done in Equation 5. That's always undefined.
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Well fine then, I will. Check back to my original post later, I'll update it with the paragraph later tonight.
Posted by: Nfested
Quote:
Originally posted by Null Actor
Dividing by zero is basic calculus - you end up with infinity.
Zero, however, is a hack.
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OMG If I had read that 2 days ago it would've helped me out in school.
0.999..... is 1. There are no numbers in between 1 and 0.999..... Therefore they are the same number.
Posted by: Lord_Buttplug
Quote:
Originally posted by Nfested
OMG If I had read that 2 days ago it would've helped me out in school.
0.999..... is 1. There are no numbers in between 1 and 0.999..... Therefore they are the same number.
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0.999... is not 1.
Posted by: TheeMon
what about .999 1/2 ...
Posted by: Lord_Buttplug
He was talking about .999 with 9s going on to infinity. This still isn't 1.
Posted by: Shalome
Yup. Even if the 9s go on to infinity, it's still not equal to 1. Faulty logic.
Posted by: Gunslinger
May I suggest that this thread be closed now?
You want to do it.
Posted by: Shalome
Nah. Much more retarded threads have gone on much longer. Why derail this stupidtrain?
Posted by: The Armpit
Saying that .99999... = 1 becuase there are no numbers inbetween it is like saying that Letter A = Letter B because there are no letters between that...
Posted by: Canis Lupus
blame the smartass who thought up the idea of rounding off numbers to the nearest whatever... that's really the cause of all this silly conjecture 
Posted by: AK47
I blame Ghetto Blasta for bringing up the topic!!
jk of course
Posted by: Spider
choo-choo !!
Posted by: Gunslinger
Someone's train of thought is still boarding at the station.
Posted by: redwench
mines in the yards.
Posted by: Cheese
Wow, I guessed I missed all the nonsense the first time with the debate about .9999 repeating...
But I remember a few math classes trying to show this a couple different ways...
If I may (even at risk of looking like a complete fool):
1/3 = .33333 repeating
2/3 = .66666 repeating
3/3 = .99999 repeating and/or 1
Posted by: Gunslinger
3/3 is a rational number.
.999999999 is an irrational number.
Posted by: Cheese
any repeating decimal is a rational number...
:edit:
That is to say, any repeating decimal can be expressed in fraction form.
Posted by: Gunslinger
No.
Posted by: Cheese
Oh ok, that clears it all up...
Posted by: Gunslinger
Non-terminating decimals are irrational.
.99999999 is a non-terminating decimal.
Posted by: Null Actor
_
.9
Posted by: redwench
1/3 is not equal to .33333...
its an approximation, the nearest we can get to it.
Posted by: Gunslinger
Yeah. I just assumed that it was understood.
Posted by: Cheese
ok wench, that makes more sense.
But Gunslinger, that's still not true. Repeating decimals are rational numbers. Irrationals are pi and e and so on. 1/9 is not irrational even though its .111...
Posted by: redwench
i thought it was too, but apparently not.
Posted by: Cheese
Christ, I'm sorry I wasn't under the assumptions the rest of you had already made. I'll definately make it a point to exclude myself from further intellectual discussions to avoid all the contempt.
Posted by: Null Actor
GS is wrong however.
If a decimal can be represented as a fraction, it is a rational number.
yes, even 0.3 repeating.
Posted by: Null Actor
To clarify 0.9 repeating might actually be irrational (I'm too lazy to attempt to even think about it, or care!), but the statement that non terminating decimals are irrational is false.
Posted by: Gunslinger
Quote:
Originally posted by Shalome
Why derail this stupidtrain?
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Christ, I'm sorry I wasn't under the assumptions the rest of you had already made. I'll definately make it a point to exclude myself from further intellectual discussions to avoid all the contempt.
There's a penny on the tracks.
Posted by: Shalome
Posted by: Cheese
Quote:
Originally posted by Gunslinger
Christ, I'm sorry I wasn't under the assumptions the rest of you had already made. I'll definately make it a point to exclude myself from further intellectual discussions to avoid all the contempt.
There's a penny on the tracks.
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Yea, I should have really kicked myself for ever questioning something I was curious about. Everyone knows curiosity killed the cat.
Posted by: Gunslinger
I was not reffering to any questioning discussing you did, rather, that you seemed to get offended over absolutely nothing.
The "I thought it was understood" comment wasn't even directed at you. I wasn't trying to slam you at all.
Yo.
Posted by: Canis Lupus
now now children ... no need to make an already silly thread even sillier...
Posted by: uh...ok
*risks his life and jumps on the train track to remove the penny and then runs back out of the way*
Anyway, this thread is interesting. Someone posted the JPG of a person with a chalk writing the 1=2 formula on a board. I think I left it at home though... 
-uh...ok
Posted by: Grimlock
Irrational numbers are decimal number in which the sequence is never EVER repeated, so 0.999 is ratinla, because itis repeated infinitely.
Posted by: Grimlock
Irrational numbers are decimal number in which the sequence is never EVER repeated, so 0.999.... is rational, because iti s repeated infinitely.
Posted by: redwench
please dont repeat your posts infinitely
Posted by: Cheese
So I've actually spent time researching this topic, and I'm still not really convinced either way.
http://www.math.lsa.umich.edu/~math...y/Equals1.shtml
This link came from a university math course, but like I said, I'm still not convinced.
Posted by: BW
man... glad life isn't like this...
Imagine trying to get from point a to point b. you're almost there, but you'll never reach it lol.
Posted by: AngstMerchant
Much like this thread and the bottom of the page. . .
Posted by: Mr. Pink
Quote:
This man speaks the truth.
Posted by: NightMage
Actually, what is being claimed as a flaw is not a flaw... (a-b) doesn't become 0 until you enter the values... but you can prove that 0=1 another way here's how
a^2-b^2 = a^2-ab
differentiate the equation
2a-2b = 2a-1
insert values
(2*1)-(2*1) = (2*1)-1
2-2 = 2-1
0=1
if anyone can see a flaw in this let me know
Posted by: uh...ok
You can't differentiate by two variables at once buddy.
You can only do d/da or d/db to everything, not d/da to one and d/db to another.
Not to mention that even if you could, differentiating ab would require you to use the product rule.
-uh...ok
Posted by: uh...ok
And (a-b) does equal zero because before that you let a=b. You don't need to insert values to prove that a variable minus itself is zero.
-uh...ok
Posted by: redwench
yes, youhawk is correct, when you differentiate wrt to different variables, you have a whole new ball o wax.
Posted by: uh...ok
And partial differentiation IS NOT FUN!!!
-uh...ok
Posted by: Kdr Kane
Quote:
Give me a break. That's not even a real definition of an equation.
This thread should be merged with the other. Nothing illuminating in this one.
Posted by: uh...ok
Hehe Kane that's not the point. The error was made a looong time before that. 
But the other thread has become a .9999...=1? thread rather than ways to prove that 1=0.
-uh...ok
Posted by: Kdr Kane
True.
But, I'd just be happy if everyone on these boards could balance their checkbook.
Or spell.
Posted by: uh...ok
Hey, I put those extra o's in "long" on purpose! 
Whatever happened to the smiley where it looks like it's paranoid! I can't find it... The one where it has one eye half open and the other eye open.
-uh...ok
Posted by: uh...ok
This one:
http://home.jps.net/~tanis/pics/suspect.gif
Except I could swear that OTS' is a little more purple than that.
-uh...ok
Posted by: Gunslinger
Also, I don't see how he factored
a^2 - b^2
into
a^2 - ab
Edit: Nevermind. He's still doing a=b stuff.
The math is flawed, regardless. Oh well.
Posted by: NightMage
lets get this straight.... we all agree that the derivative of a^2 is 2a right?.... and i agree i did make a mistake differentiating ab.... it should have ended up as a+b
so the equation would have read 2a-2b = 2b-(a+b)
and yeah i forgot that he had already defined a=b, therefore making it a-a. so the result is wrong.... sorry guys. i didn't prove that 0 = 1 i proved that 0 = 0 lol.
I hate little stuff-ups like that
Posted by: Shalome
Sorry, guys... this belongs merged with the original thread.
Posted by: redwench
good move there shal
Posted by: uh...ok
Nightmage, it's not the derivation that's incorrect - it's the fact that you tried to derive with respect two different variables in the same equation.
Basically this is the way you derived the equation:
f(a,b) = a^2 + b^2 = a^2 - ab
d/d(a or b???) f(a,b) = (d/da)a^2 + (d/db)b^2 = (d/da)a^2 - (d/d[a or b???])ab
Obviously that does not even make any sense at all. Even if you ignore the fact that you have d/da and d/db scattered arbitrarily across the equation, what are you actually taking the entire equation with respect to, and what are you taking ab with respect to?
If I had the equations:
f(a,b) = a^2 + b^2 and g(a,b) = a^2 + ab
I can't just say that:
f'(a,b) = 2a + 2b and g(a,b) = 2a + (a + b)
You have to differentiate the equation one variable at a time. When you do so, you simply treat the other variable as a constant. So when you take the derivative of f(a,b) you actually end up with 2 equations:
f sub a = 2a
f sub b = 2b
and for g(a,b)
g sub a = 2a + b
g sub b = a
But that's something you don't need to know yet... you'll learn it in Multivariable Calculus.
BUT if you're already in Single Variable Calculus, you DO have to realize that you canNOT take the derivative with respect to both a and b in the same equation at the same time - especially when it's so arbitrary and picking which variables in the equation you take d/da to and which ones you take d/db to.
-uh...ok
Posted by: Null Actor
Our little MIT genius.
You realize uhok that when I start tearing in to OpenCourseWare, you are gonna be on my hit list of people to bother.
Posted by: uh...ok
I must correct myself: there actually IS a way to do stuff like that in Single-Variable Calculus. It's called a differential.
Here's a popular example that Calc tests like to use:
Given: C = x^2 + xy - y^2, find dy/dx. (where C is some constant)
In this case you take the derivative with respect to x.
(d/dx) C = 2x + (x*dy/dx + y) - 2y(dy/dx)
which gives you:
0 = 2x + x(dy/dx) + y - 2y(dy/dx)
Move the variables without (dy/dx) components to one side and the variables with it on the other:
2y(dy/dx) - x(dy/dx) = 2x + y
(dy/dx) (2y - x) = 2x + y
dy/dx = (2x + y)/(2y - x)
There. You can go back to your Calc or Precalc class and show that off.
-uh...ok
Posted by: Freak
I hope that made sense to someone.
I feel like an ignorant philistine now.
Edit: ok the second part makes sense now that its in plain algebra =)
Posted by: uh...ok
Nova I think I'd end up learning more from you than vice versa, so beware! (and bring it on!)
And I'm no genius. I feel stupid because these problem sets are just confusing the hell out of me.
That's why I like actually typing up all that shit.. it's all stuff I understand - and it takes my mind away from the stuff I DON'T understand.... not to mention that girl next door.
-uh...ok
Posted by: Gunslinger
I understand it, but I've had a whole lot of Calculus.
Posted by: uh...ok
Gunny you probably know a lot more than me. Except I remember easy stuff like that better because it's a lot more recent to me than it is to you.
-uh...ok
Posted by: Cheese
Quote:
Originally posted by uh...ok
I must correct myself: there actually IS a way to do stuff like that in Single-Variable Calculus. It's called a differential.
-uh...ok
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I learned that to be Implicit Differentiation.
Posted by: uh...ok
Hrm... I WAS having trouble remembering the term... I think you got it Cheese.
I wonder why I thought "differentials" could have been the right term. Oh well. Teaches a valuable lesson: when it doubt, look it up!
-uh...ok
Posted by: NightMage
Ok I think I understand it all now ... at the moment I'm doing pre-uni calc. (australia) and it's all basic diff. and so forth. I felt so sure I had it right.
Posted by: The_Turks(ff7)
Quote:
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Irrational numbers are decimal number in which the sequence is never EVER repeated, so 0.999.... is rational, because iti s repeated infinitely.
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irrational numbers are nonrepeating AND nonterminating decimals. The decimal never ends but never repeats.
Posted by: Cheese
Quote:
Originally posted by uh...ok
Hrm... I WAS having trouble remembering the term... I think you got it Cheese.
I wonder why I thought "differentials" could have been the right term. Oh well. Teaches a valuable lesson: when it doubt, look it up!
-uh...ok
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It's cool. I wasn't too sure either, but I do know that differential equations is my next course in math.
Posted by: Erekose
that reminds me... i have two weeks worth of math to catch up on. damn you all, damn you all to the 'hell of REEAAALLLY big number and equations with no solutions'
Posted by: uh...ok
Erek, that hell you speak of sounds familiar... oh wait, my problem sets.
-uh...ok
Posted by: Cheese
Hell, I'd give anything for some serious help before my discrete math mid-term this friday...
Posted by: uh...ok
Discrete math sucks, at least from what I've heard of it.
I hopefully won't have to take it.
-uh...ok
Posted by: Ghetto Blasta
You crazy kids and your "Calc" and your "Pre-Calc"! I don't take Pre-Calc till next year!
Actually, next year I get to take Pre-Calc AND Calc. That'll be a trip. See, before Pre-Calc we have to take Math Courses 1 - 3. I took 1 in 8th grade, but the teacher was a nut and gave 2 question test with no partial credit, and just had no clue what she was doing. So I got a 65 in the course and a 70 on the regents. Both passing grades, but my mom was like "That's not good enough! You must take the class again!" and so I was doomed to repeat Course 1 in 9th.  I got a 98 in the course. Stupid parental unit. ANYWAY, so now I'm a junior in Course 3, instead of Pre-Calc with the rest of the kids on my level. So if i want to take Calc, which I do, I have to take both in the same year.
Posted by: Cheese
Is Pre-Calc actually a pre-req for Calc? If not, in your position I wouldn't even recommend taking it. You'll have to work just a little bit harder, but looking back, Pre-Calc was a pretty useless class.
Posted by: redwench
not if youre going to take physics in college. youll need it for that.
Posted by: Cheese
I'm taking physics in college right now...its calculus based. Pre-calc for me was essentially Algebra 2/Trig over again with a little elaboration on each section.
Posted by: redwench
yes, now that i think of it, its not until statics and mechanics that you get heavily into the directional and trig crap.
Posted by: Ghetto Blasta
Well see, here in NY we don't have classes like Algebra or Geometry. We have Courses 1 - 3, then precalc ect.
actually, i'm the last class to use the course 1 - 3 system. now it's just Math A for 2 years and Math B for two years.
Each course has a combo of everything from algebra to constructions. Each year builds on what you learned in the previous year. So in Course 1 you'd do factoring polynomials and that sort of thing, then in Course 2, you'd do quadratic equations.
And yes, precalc is a pre-req for Calc. but apparently I'll learn things in Pre-Calc before I'll need them in Calc.
Posted by: uh...ok
Pre-Calc and Calc are actually... well in a lot of ways they're not too related. I mean in Calculus you learn about differentiation and integration, mainly. That's why it's called Differential Calculus and Integral Calculus... with Pre-Calc (otherwise known as Math Analysis), the focus is a bit more on Trig, vector functions, and... God, I don't even remember what I learned in Math Analysis.
You'd definitely have an easier time in Calc if you took Pre-Calc BEFORE it... but if the courses are modeled right, it's possible to take them simultaneously. For example, as long as you learn vector operations before getting into Vector Calculus... you're fine...
-uh...ok
Posted by: Grimlock
heh, all that made sense to me, it's just a pity that it didn't BEFORE I failed Advanced-Maths, pure and applied.
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