Proof that 2 = 1???

let a = b

a² = ab Multiply both sides by a

a² + a² - 2ab = ab + a² - 2ab Add (a² - 2ab) to both sides

2(a² - ab) = a² - ab Factor the left, and collect like terms on the right

2 = 1 Divide both sides by (a² - ab)

Now, is it just me or does this look correct? I found it here http://mcraefamily.com/MathHelp/JokeProofFactoring.htm where it states thats its not real, but I can't see whats wrong with it.

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Reply 1

dvs

Since a=b then a^2 - ab = a^2 - a^2 = 0. So it's basically the old division by zero trick.

Reply 2

Dan R

Almost... But a² - ab = 0. It doesn't make sense to divide by 0!

Reply 3

idoit

For years now mathematicians have suppressed the truth of 2=1, not convinced by that proof, try this one:

y = x^2 ∴ dy/dx = 2x

y = x^2 = x*x = x + x + x.... ∴ dy/dx = 1 + 1 + 1... = x

∴2x = x

∴2 =1

QED

Reply 4

dvs

And of course we can conclude that 2=-1 because 1=-1.

-1 = -1
1/-1 = -1/1
sqrt(1/-1) = sqrt(-1/1)
1/i = i/1
1 = i^2
1 = -1

Reply 5

idoit

And if 2 = -1 then (2 + 4)/3 = (-1 + 4)/3 therefore 2 = 1!!!!!

Reply 6

Esquire

x=1
x^2=x
(x^2)-1=x-1
(x-1)(x+1)=(x-1)
x+1= (x-1)/(x-1)
x+1=1
1+1=1
2=1 :biggrin:

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You cant actually prove that 2=1, it's a basic mental construct called an axiom that we accept as true in order to do maths :biggrin:

Reply 7

Angel Interceptor

DaneC

This is rubbish - you're dividing by sero.

Reply 8

Manifest

idoit

QED

Have forgotten...What does it mean?

Reply 9

idoit

quod erat demonstrandum - that which was to be proved.

Reply 10

Esquire

I wrote that on a show that question out in full in my C2 exam cos i finished early. Anyway... I subsequently found out that I was wrong, and sent off to get a copy of the script. The examiner had written "so close, but no banana"

Hehehe

idoit

Could someone explain this one?

Reply 13

yazan_l

Esquire

x=1
x^2=x
(x^2)-1=x-1
(x-1)(x+1)=(x-1)
x+1= (x-1)/(x-1)
x+1=1
1+1=1
2=1 :biggrin:

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You cant actually prove that 2=1, it's a basic mental construct called an axiom that we accept as true in order to do maths :biggrin:

here again u r dividing by zero...

Reply 14

AlphaNumeric

e-unit

Could someone explain this one?

How can you have "x" lots of x? You can have 2 lots of x, 5 lots of x, but how do you add together x lots of x? It's an undefined sequence.

Reply 15

Simba

cos²x + sin²x ≡ 1
cos²x ≡ 1 - sin²x
cos x ≡ √(1 - sin²x)
1 + cos x ≡ 1 + √(1 - sin²x)

Sub. x = pi

1 - 1 = 1 + √(1 - 0²)
0 = 2

Spoiler

Reply 16

Zthavan

Simba

cos²x + sin²x ≡ 1
cos²x ≡ 1 - sin²x
cos x ≡ √(1 - sin²x)
1 + cos x ≡ 1 + √(1 - sin²x)

Sub. x = pi

1 - 1 = 1 + √(1 - 0²)
0 = 2

Spoiler

]

Taking square roots requires the use of the double plus-or-minus sign (or absolute values). In this case, the plus sign gives an odd result, and the minus sign is the one that gives the right conclusion

Reply 17

super_baros

idoit

sometimes my teacher does
∴2x = x

∴2 =1
///
QED

What do the three lines mean?...

Reply 18

john-boro

it just shows how ridiculous all of these supposed 'proofs' are, because in essence you are performing an invalid mathematical calculation. If 2x=x then it is not valid to divide by x, because it is zero.
I think your teacher is being ironic. :smile:

Reply 19

super_baros

john-boro