Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**dreamalot****Member**- Registered: 2009-04-25
- Posts: 2

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

Offline

**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

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.

Offline

**dreamalot****Member**- Registered: 2009-04-25
- Posts: 2

No exams. Just curious.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,813

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)*

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

Offline

**DarkLightA****Member**- Registered: 2009-05-27
- Posts: 16

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

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

Offline

**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Here is another proof that 1 = 2, one that doesnt make use of division by 0.

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,813

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)*

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,093

Here is another:-

But this proves 2 > 3.

3 < 2

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**amhore13****Member**- Registered: 2009-08-03
- Posts: 5

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.

Offline

**amhore13****Member**- Registered: 2009-08-03
- Posts: 5

can you proof 1=0

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,813

Hi amhore;

Jane wrote:

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)*

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

Offline

**manzil****Member**- Registered: 2009-07-12
- Posts: 1

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,813

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.**

Offline

**amhore13****Member**- Registered: 2009-08-03
- Posts: 5

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..

Offline

**santhosh****Member**- Registered: 2010-07-19
- Posts: 14

amhore13 wrote:

can you proof 1=0

pls tell me how it will get

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,813

Hi santhosh;

JaneFairfax wrote:

Jane wrote: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.**

Offline

**jk22****Member**- Registered: 2010-06-14
- Posts: 33

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)*

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,613

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.

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

Offline

**jk22****Member**- Registered: 2010-06-14
- Posts: 33

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)*

Offline

**sur_arijit01****Member**- Registered: 2011-05-06
- Posts: 1

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

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,613

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 bundy (2011-05-06 06:45:09)*

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

Offline

**joker30****Guest**

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****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,813

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.**

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,613

hi joker30

OK, but it's still a case of:

in post #18, I wrote:

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 bundy (2011-06-19 05:00:55)*

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

Offline

**reconsideryouranswer****Member**- Registered: 2011-05-11
- Posts: 171

ganesh wrote:

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:

Signature line:

I wish a had a more interesting signature line.

Offline