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careless25
2012-08-09 12:37:52

Heres an infinite series "proof" that shows 0 = 1

0 = 0 + 0 + 0 + 0 + · · ·
= (1 − 1) + (1 − 1) + (1 − 1) + (1 − 1) + · · ·
= 1 − 1 + 1 − 1 + 1 − 1 + 1 − 1 + · · ·
= 1 + (−1 + 1) + (−1 + 1) + (−1 + 1) + · · ·
= 1 + 0 + 0 + 0 + · · ·
= 1

"Legend has it that, around 1703, in letters to contemporary mathematicians, an Italian monk by the name of Guido Grandi (often called Guido Ubaldus) presented this as proof of the existence of God, since it suggested that the universe could have been created out of nothing! What he actually meant isn't clear, but we do know that the brightest minds of the day were unsure how to explain what the problem was. Leibniz at least recognized that the problem was in the ____ line above;"

I left it blank intentionally

This is copied from my Calculus prof notes, he showed is this "proof" in class.

anonimnystefy
2012-08-01 21:33:59

Hi cmowla

Yes, you are right.

cmowla
2012-08-01 14:44:26

#### anonimnystefy wrote:

Hi Ashok123

Your steps aren't algebraicly correct. How did you get that a^2-a^2=a(a-a) ?

The only flawed step was when he divided by

.  Everything else is correct.

anonimnystefy
2012-07-31 19:17:47

Hi Ashok123

Your steps aren't algebraicly correct. How did you get that a^2-a^2=a(a-a) ?

Ashok123
2012-07-31 19:04:44

#### dreamalot wrote:

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

a=a

=
(since, multiply both side with "a")

-
=
-
(since,
-
=(a+b)(a-b))
(a-a)(a+a)=a(a-a)
a+a=a
2a=a
2=1

2011-06-20 04:15:59

#### 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:

bob bundy
2011-06-20 02:58:43

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

bobbym
2011-06-20 02:35:39

Hi joker30;

Welcome to the forum!

That is a little bit of a twist!

joker30
2011-06-20 01:54:29

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

bob bundy
2011-05-07 04:39:21

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.

sur_arijit01
2011-05-07 04:07:33

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

jk22
2010-08-09 00:07:30

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

bob bundy
2010-08-07 07:03:55

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.

jk22
2010-08-07 06:19:29

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).

bobbym
2010-07-20 05:31:04

Hi santhosh;

#### 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.

She is even more correct!

Welcome to the forum!