Today, I have proof that 2=1!
21-01-2009, 08:27 PM
#1
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Today, I have proof that 2=1!
Following on from my previous post not that long ago on pythagoras, I came across this rather amusing little equation.
It only makes use of fundamental algebra, but an error allows this result. See what you make of it.
Let us say that we know that a = b
Now multiply both sides by a, that leaves you
a˛ = ab
Now add a˛ - 2ab to both sides, which leaves you
a˛ + a˛ - 2ab = ab + a˛ - 2ab
which simplifies to
2(a˛ - ab) = a˛ - ab
Now divide both sides by a˛ - ab
2 = 1
Discuss/ spot the problem!
JJ
It only makes use of fundamental algebra, but an error allows this result. See what you make of it.
Let us say that we know that a = b
Now multiply both sides by a, that leaves you
a˛ = ab
Now add a˛ - 2ab to both sides, which leaves you
a˛ + a˛ - 2ab = ab + a˛ - 2ab
which simplifies to
2(a˛ - ab) = a˛ - ab
Now divide both sides by a˛ - ab
2 = 1
Discuss/ spot the problem!
JJ
Last edited by JjCoDeX75; 21-01-2009 at 08:31 PM.
21-01-2009, 08:34 PM
#5
Following on from my previous post not that long ago on pythagoras, I came across this rather amusing little equation.
It only makes use of fundamental algebra, but an error allows this result. See what you make of it.
Let us say that we know that a = b
Now multiply both sides by a, that leaves you
a˛ = ab
Now add a˛ - 2ab to both sides, which leaves you
a˛ + a˛ - 2ab = ab + a˛ - 2ab
which simplifies to
2(a˛ - ab) = a˛ - ab
Now divide both sides by a˛ - ab
2 = 1
Discuss/ spot the problem!
JJ
It only makes use of fundamental algebra, but an error allows this result. See what you make of it.
Let us say that we know that a = b
Now multiply both sides by a, that leaves you
a˛ = ab
Now add a˛ - 2ab to both sides, which leaves you
a˛ + a˛ - 2ab = ab + a˛ - 2ab
which simplifies to
2(a˛ - ab) = a˛ - ab
Now divide both sides by a˛ - ab
2 = 1
Discuss/ spot the problem!
JJ
i spot it...
a+b are letters not numbers...
you cant fool me that easily
21-01-2009, 08:35 PM
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21-01-2009, 08:43 PM
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No, I simply mean that I have worked the previous line into a slightly easier format, and that is correct.
You are close to the problem, but that isnt it.
Jtech - all good this end, though nothing new to report - we must catch up at some point.
You are close to the problem, but that isnt it.
Jtech - all good this end, though nothing new to report - we must catch up at some point.
21-01-2009, 08:52 PM
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Hi bud
Yup - if you deduct 2ab from ab, you would indeed be left with -ab.
As far as the brackets is concerned, in that instance, 2ab would be the same as 2(ab), as in maths rules, the a would be multiplied by the b and then the product would be multiplied by the 2.
but dont forget that a X b X c = a X (b X c) = (a X b) x C if it helps!
JJ
Yup - if you deduct 2ab from ab, you would indeed be left with -ab.
As far as the brackets is concerned, in that instance, 2ab would be the same as 2(ab), as in maths rules, the a would be multiplied by the b and then the product would be multiplied by the 2.
but dont forget that a X b X c = a X (b X c) = (a X b) x C if it helps!
JJ
21-01-2009, 08:53 PM
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BINGO!
That is the exact problem! Well done!
It was used as an example of the type of errors that occur in mathematics when trying to prove theorems.
What surprised me was how utterly believable the equation appears!
JJ
That is the exact problem! Well done!
It was used as an example of the type of errors that occur in mathematics when trying to prove theorems.
What surprised me was how utterly believable the equation appears!
JJ
21-01-2009, 08:55 PM
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to be fair, you can divide by zero - it just leads to an irrational number, namely infinity.
If you divide 2 by 0 = infinity, and also 1 by zero also is infinity. Therefore, the equation still kinda stays faithful to the rules of maths, but is still quite wrong!
JJ
If you divide 2 by 0 = infinity, and also 1 by zero also is infinity. Therefore, the equation still kinda stays faithful to the rules of maths, but is still quite wrong!
JJ
21-01-2009, 08:55 PM
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yeah confused me too, but had to try and work it out!
That was a relatively simple one too, I can only imagine some of the mistakes that could happen when proving really complex theorems
Gave me something to do anyway, now back to the revision
lol
21-01-2009, 08:56 PM
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21-01-2009, 08:58 PM
#20
Benni, in your attempt to be sarcastic, you slipped up by using the word 'result' when you should really have been using the word 'resort' instead.
Cheers,
Grant
p.s: waiting for in return because I've made some sort of error.
p.p.s: I also have no idea about the question asked by the OP, so as you can see, I have also resorted to a sarcastic reply.
Cheers,
Grant
p.s: waiting for
in return because I've made some sort of error.p.p.s: I also have no idea about the question asked by the OP, so as you can see, I have also resorted to a sarcastic reply.
21-01-2009, 09:01 PM
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21-01-2009, 09:03 PM
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Benni, in your attempt to be sarcastic, you slipped up by using the word 'result' when you should really have been using the word 'resort' instead.
Cheers,
Grant
p.s: waiting for in return because I've made some sort of error.
p.p.s: I also have no idea about the question asked by the OP, so as you can see, I have also resorted to a sarcastic reply.
Cheers,
Grant
p.s: waiting for
in return because I've made some sort of error.p.p.s: I also have no idea about the question asked by the OP, so as you can see, I have also resorted to a sarcastic reply.
Benni.
P.S: I've gone over your reply many times and I can find no errors, which has annoyed me greatly.
21-01-2009, 10:24 PM
#25
Audio specialist
minus one... square roooted. = J incomprhendable numbers given letters.. J or I before we used that for current in electronics.
2 is the only even prime.
But the total number of primes is infinite.
Therefore the probability that a given prime number is even is 1 over infinity, or zero.
Hence it's impossible for a prime number to be even — and 2 does not exist.
2 is the only even prime.
But the total number of primes is infinite.
Therefore the probability that a given prime number is even is 1 over infinity, or zero.
Hence it's impossible for a prime number to be even — and 2 does not exist.
Last edited by biglee; 21-01-2009 at 10:47 PM.
22-01-2009, 12:08 AM
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This type of error is called "straying into absurdity". What happens is you introduce infinity into both sides of the equation since 0 will go into a finite number and infinite amount of times. Dividing by zero in the mathematical world is simply undefined so therefore the equation cannot hold any more. This type of error creeps into many proofs that mathematicians try to create. Very subtle and very easy to make this sort of error.
22-01-2009, 12:17 AM
#27
To find the issue, I just replaced B with A, like you said I could at the beginning, which made it all pretty fucking obvious TBH as you end up with dividing by (A˛ - A˛) which to anyone is very obviously zero, lol
If you hadnt said there was a problem though, and just asked me to check your work on a line by line basis, I would have said each line was correct without a doubt, so it certainly proves what you wanted to, the danger of proving things without paying enough attention as id have never noticed it until the 2=1 bit where obviously it had to be wrong.
If you hadnt said there was a problem though, and just asked me to check your work on a line by line basis, I would have said each line was correct without a doubt, so it certainly proves what you wanted to, the danger of proving things without paying enough attention as id have never noticed it until the 2=1 bit where obviously it had to be wrong.
22-01-2009, 01:15 AM
#28
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Following on from my previous post not that long ago on pythagoras, I came across this rather amusing little equation.
It only makes use of fundamental algebra, but an error allows this result. See what you make of it.
Let us say that we know that a = b
Now multiply both sides by a, that leaves you
a˛ = ab
Now add a˛ - 2ab to both sides, which leaves you
a˛ + a˛ - 2ab = ab + a˛ - 2ab
which simplifies to
2(a˛ - ab) = a˛ - ab
Now divide both sides by a˛ - ab
2 = 1
Discuss/ spot the problem!
JJ
It only makes use of fundamental algebra, but an error allows this result. See what you make of it.
Let us say that we know that a = b
Now multiply both sides by a, that leaves you
a˛ = ab
Now add a˛ - 2ab to both sides, which leaves you
a˛ + a˛ - 2ab = ab + a˛ - 2ab
which simplifies to
2(a˛ - ab) = a˛ - ab
Now divide both sides by a˛ - ab
2 = 1
Discuss/ spot the problem!
JJ
hence 2=2
22-01-2009, 09:36 AM
#29
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Hi Chip - we must catch up at some point. I will try to remember to bell you tomorrow rather than mid week!
Ref the below - you are spot on. The error you could argue was to continue with b defined as b, as opposed to reverting it to a, which would simply prevent the error from occuring, but I must say that what I liked about the above example of error is that it is so persuasive on face value!
The good news for everybody is that I have nearly finished the book I am on, so there should be no more silly maths for a bit!
The next one is on the concept of infinity! So that will be fun!
JJ
biglee - my only critism is that you are using both maths and statistics to prove that 2 doesnt exist. You are correct that there are an infinite number of prime numbers (as I believe that this has been proved), but you are only stating that Statistically 2 is unlikely to exist. Given that we can prove that 2 does exist (though please dont ask me to!), the statistics can be disregarded!
Even so - I like the logic!
JJ
Ref the below - you are spot on. The error you could argue was to continue with b defined as b, as opposed to reverting it to a, which would simply prevent the error from occuring, but I must say that what I liked about the above example of error is that it is so persuasive on face value!
The good news for everybody is that I have nearly finished the book I am on, so there should be no more silly maths for a bit!
The next one is on the concept of infinity! So that will be fun!
JJ
biglee - my only critism is that you are using both maths and statistics to prove that 2 doesnt exist. You are correct that there are an infinite number of prime numbers (as I believe that this has been proved), but you are only stating that Statistically 2 is unlikely to exist. Given that we can prove that 2 does exist (though please dont ask me to!), the statistics can be disregarded!
Even so - I like the logic!
JJ
To find the issue, I just replaced B with A, like you said I could at the beginning, which made it all pretty fucking obvious TBH as you end up with dividing by (A˛ - A˛) which to anyone is very obviously zero, lol
If you hadnt said there was a problem though, and just asked me to check your work on a line by line basis, I would have said each line was correct without a doubt, so it certainly proves what you wanted to, the danger of proving things without paying enough attention as id have never noticed it until the 2=1 bit where obviously it had to be wrong.
If you hadnt said there was a problem though, and just asked me to check your work on a line by line basis, I would have said each line was correct without a doubt, so it certainly proves what you wanted to, the danger of proving things without paying enough attention as id have never noticed it until the 2=1 bit where obviously it had to be wrong.
22-01-2009, 10:10 AM
#32
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Like your style! 
- Also like the edison comment - that is class!
Chip - noted, big fella - I will see if I can get my brain to remind me! (odds on that I forget and call u in the morning!)
JJ
- Also like the edison comment - that is class!Chip - noted, big fella - I will see if I can get my brain to remind me! (odds on that I forget and call u in the morning!)
JJ
22-01-2009, 12:33 PM
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Is so true though. Ask any mathematician, even the most knowledgeable and most phenomenal. The more you learn and study maths, the more you realise how much MORE there is to learn.
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