Is two equals one?
Is 2 = 1?
Today, I will prove that two is equal to one (2 = 1). I will do that in more than one way. You know what you have to do? You have to point out the fallacy in the proofs.
The Fallacious Proof - 1:
Let, a = x
a+a = a+x [add a to both sides]
2a = a+x [a+a = 2a]
2a-2x = a+x-2x [subtract 2x from both sides]
2(a-x) = a+x-2x [2a-2x = 2(a-x)]
2(a-x) = a-x [x-2x = -x]
2 = 1 [divide both sides by a-x]
Hence Proved
The Fallacious Proof - 2:
Let, a = b
a^2 = ab [multiplying ‘a’ both sides]
a^2 – b^2 = ab – b^2 [subtracting b^2 from both sides]
(a+b)(a-b) = b(a-b) [dividing both sides by (a-b)]
a+b = b
b+b = b [since a=b, replacing a by b]
2b = b
2 = 1 [dividing both sides by b]
Hence Proved
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November 10th, 2011 - 18:43
now i will give another proof that u cant neglect…….
we know
-2=-2
4-6=1-3
4-6+(9/4)=1-3+(9/4) [adding 9/4 on both sides]
[2-(3/2)]^2=[1-(3/2)]^2 [by using (a-b)^2]
2-(3/2)=1-(3/2) [square root on both sides]
2=1 hence proved
August 12th, 2011 - 15:00
in proof 2nd also :
dividing by (a-b) is not justifiable as “a=b”
(a+b)(a-b) = b(a-b) [dividing both sides by (a-b)
it is wrong
August 12th, 2011 - 14:58
your ans is wrong becous ” a = x ” so and so (a-x = 0) and we can’t divide by it…
September 11th, 2010 - 19:30
a-b is divided which is equal to 0. In mathematics number divided by 0 is undefined. This equation cannot go further after step 4.
August 28th, 2010 - 21:32
in both the proofs ur diving both sides by quantities equalling to zero i.e—(a-x) & (a-b)
August 22nd, 2010 - 19:58
well i am a science maths student and even then couldn’t get the trick. i plan to try this on our institute teacher let’s see if it works………well this is cool
August 12th, 2010 - 20:59
WHAT EXACTLY YOU ARE DOING IS THAT YOU ARE MULTIPLYING A QUANTITY WITH ZERO AND THEN CANCELING OUT THE ZERO WHICH IS RUBBISH
August 7th, 2010 - 14:16
dear brother
to subtract a nummber ffrom two addition numbers
we wnat to put the bracket
(a+x)-2x
August 6th, 2010 - 07:47
rocking
July 31st, 2010 - 17:42
Division by ZERO is not defined.
In the above two ways of proof division is done by ZERO.
Hence the proof is false.
July 31st, 2010 - 11:16
in proof 2nd also :
dividing by (a-b) is not justifiable as “a=b”
July 31st, 2010 - 11:13
in proof 1st :
dividing by (a-x) is not justifiable as “a=x” which means (a-x)=0
July 27th, 2010 - 12:02
Basic RUle:when u divide a equation both side by some number,it should not be ZERO.
In d first proof ur dividing both side by (a-x),so that means a is not equal to x,but ur 1st assumption is that a=x.
and in d same way in the second proof,ur dividing with (a-b),so that impies a should not be equal to b,but in the very next step ur using the condition a=b.
July 27th, 2010 - 10:55
You can’t divide a number by zero. In this proof a is made equal to b and then division is carried out by (a-b) which is just another way of dividing by zero and thus is not permissible in mathematics.
July 27th, 2010 - 10:45
Too Good. I like such proofs. Thanks to this site.
December 23rd, 2010 - 18:38
you dont know about the maths please read its basic and then comments