Math Is Fun Forum

dreamalot

Member

Registered: 2009-04-25

Posts: 2

1=2 proof

Hey, swim is new here and is wondering if someone could direct him to the classic 1=2 proof? Thanks.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: 1=2 proof

Why do you want to learn incorrect proofs? Much better if you just concentrate on learning correct proofs. That might help you pass your exams.

dreamalot

Member

Registered: 2009-04-25

Posts: 2

Re: 1=2 proof

No exams. Just curious.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 1=2 proof

Hi dreamalot;

   I'm afraid Jane is right about learning correct proofs but if you are determined to see this, here is a link that I know of.
http://en.wikipedia.org/wiki/False_proof

Last edited by bobbym (2009-05-14 17:32:18)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

DarkLightA

Member

Registered: 2009-05-27

Posts: 16

Re: 1=2 proof

That's the first false proof I've found the fault in

Division by 0.. (a-b), where a=b

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: 1=2 proof

Here is another  “proof” that 1 = 2, one that doesn’t make use of division by 0.

Last edited by JaneFairfax (2009-06-12 23:05:48)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 1=2 proof

Hi Jane;

I know you are not posing this as a problem but

Line 1 identity
Line 2 identity

As near as I can figure the problem is with the third statement, the taking of the square root of both sides.

which is only true for

Last edited by bobbym (2009-06-13 18:17:15)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Re: 1=2 proof

Here is another:-
But this proves 2 > 3.

3 < 2

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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amhore13

Member

Registered: 2009-08-03

Posts: 5

Re: 1=2 proof

hi friends im just  new member of this website..i love math very much. i join here just to know what makes math simple and remembering all about math...i hope somebody can help me in this. thanks.

amhore13

Member

Registered: 2009-08-03

Posts: 5

Re: 1=2 proof

can you proof 1=0

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 1=2 proof

Hi amhore;

Why do you want to learn incorrect proofs? Much better if you just concentrate on learning correct proofs. That might help you pass your exams.

She is still right.

About half way down the page.
click me for false proofs

Last edited by bobbym (2009-08-04 05:32:39)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

manzil

Member

Registered: 2009-07-12

Posts: 1

Re: 1=2 proof

Hi friends i am just a new member of this web site.i love math very much. i am intrested in incorrect proof.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 1=2 proof

Welcome manzil

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

amhore13

Member

Registered: 2009-08-03

Posts: 5

Re: 1=2 proof

hi manzil i like the message that you so try to seek or solve my given problem proof that 1=0: its just a play dont be too serious in everything remember that my is not hard just play it around so you can learn everything....ok  just relax friends..

santhosh

Member

Registered: 2010-07-19

Posts: 14

Re: 1=2 proof

can you proof 1=0

pls tell me how it will get

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 1=2 proof

Hi santhosh;

Why do you want to learn incorrect proofs? Much better if you just concentrate on learning correct proofs. That might help you pass your exams.

She is still right.

She is even more correct!

Welcome to the forum!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

jk22

Member

Registered: 2010-06-14

Posts: 33

Re: 1=2 proof

Hi,

we have not 1=2, except if units are e.g. $ and £ in the year (to find, e.g. in the y 1976, or 1978 http://www.miketodd.net/encyc/dollhist.htm)...1£=2$ were at some time of the story of humanity.

but we were allowed to write

2 is equivalent to 0 (modulo 2)

divide by 2 and

1 is equivalent to 0 (modulo 1).

Last edited by jk22 (2010-08-06 08:51:45)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: 1=2 proof

Actually, I don't think there's any harm studying 'false' proofs as long as you're aware that there is something wrong with the proof.

That way you learn something about what is allowable in a proof and what isn't.

In the example that started this thread, for example, you should learn that dividing by zero is not acceptable in algebra.

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

jk22

Member

Registered: 2010-06-14

Posts: 33

Re: 1=2 proof

Hi,

yes, or 0^0.

Studying false proof can help not making them. Some pitfall are : 

a) right deduction, but hypotheses aren't (Sometimes proven after),    hence we can deduce nothing

b) the proof uses the result to be proven

Last edited by jk22 (2010-08-08 02:09:14)

sur_arijit01

Member

Registered: 2011-05-06

Posts: 1

Re: 1=2 proof

plz help me 2 find out the wrong step:all digits are equal just putting values of x,y
s1)  -x.y=-x.y
s2)  x^2-x(x+y)=y^2-y(x+y)
s3)  x^2-2x(x+y)/2+{(x+y)/2}^2 = y^2-2y(x+y)/2+{(x+y)/2}^2
s4)  {x-(x+y)/2}^2 = {y-(x+y)/2}^2
s5)  x-(x+y)/2 = y-(x+y)/2
s6)  x=y

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: 1=2 proof

hi sur_arijit01

It looks to me like S4 -> S5 is the faulty step.

Just because a^2 = b^2 you may not conclude that a = b  eg.  9 = 9 but + 3 is not equal to -3

But if you write

s5)  x-(x+y)/2 = -(y-(x+y)/2)

then you get x + y = x + y which seems more reasonable.

Bob

footnote:  When I'm trying to track down an algebraic error the following sometimes works.

Choose a value for x and another for y.  (Best to avoid 0 and 1 here)

If the value of the LHS = RHS then there's a strong chance the steps to that point are OK.

When LHS not = RHS you know a false step has occurred.

Last edited by Bob (2011-05-06 06:45:09)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

joker30

Guest

Re: 1=2 proof

You can proof substitution with number, no need to let x=y.

10² = 100 (right)
10²-10²=100-100
(10-10)(10+10)=10(10-10)
So,
(10+10)=10
20=10
2=1

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 1=2 proof

Hi joker30;

Welcome to the forum!

That is a little bit of a twist!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: 1=2 proof

hi joker30

OK, but it's still a case of:

In the example that started this thread, for example, you should learn that dividing by zero is not acceptable in algebra.

except substitute 'number calculations' for 'algebra'.

Bob

Last edited by Bob (2011-06-19 05:00:55)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

reconsideryouranswer

Member

Registered: 2011-05-11

Posts: 171

Re: 1=2 proof

Here is another:-
But this proves 2 > 3.

3 < 2

You're missing required grouping symbols, ganesh.

One of the lines above can be fixed by typing:

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