2=1

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Zaraden
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2=1

Postby Zaraden » Fri Nov 02, 2007 4:17 am UTC

Maybe some of you have seen this before, but I thought it was pretty cool, at least until you know what's wrong with it...



a = b --------------------------(ex. a=1, b=1)
a+a = a+b --------------------(adding a to both sides)
2a = a+b ---------------------(substituting a+a for 2a)
2a-2b = a+b-2b --------------(subtracting 2b from both sides)
2 (a-b) = a+b-2b --------------(substituting 2a-2b for 2 a-b)
2(a-b) = a-b-------------------(substituting b-2b for -b)
2=1-----------------------------(divide both sides by a-b)


Anyone see it?
Last edited by Zaraden on Fri Nov 02, 2007 5:02 am UTC, edited 1 time in total.
Let epsilon be less than zero...

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Re: 2=1

Postby Robin S » Fri Nov 02, 2007 4:20 am UTC

This one's pretty hard to search for because

You must specify at least one word to search for. Each word must consist of at least 3 characters
but I'm fairly sure it's been done before. The mistake is of course that

Spoiler:
if a = b then a-b = 0 so you can't divide by it.
This is a placeholder until I think of something more creative to put here.

SenseiJinx
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Re: 2=1

Postby SenseiJinx » Fri Nov 02, 2007 4:22 am UTC

*sigh* I'm sorry, but the
Spoiler:
dividing by 0 trick got old the first sixteen times I saw a "brain teaser" with it.


:)

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Mathmagic
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Re: 2=1

Postby Mathmagic » Fri Nov 02, 2007 4:45 am UTC

viewtopic.php?f=17&t=8119

It's weird... every time someone makes this topic (on false proofs), they always start with the 2=1 "proof".

EDIT: To clarify - this topic has already been done. There is a thread on it with a good amount of replies, on the second page. I have linked to said topic. Plz lock nao.
Last edited by Mathmagic on Fri Nov 02, 2007 3:44 pm UTC, edited 1 time in total.
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Zaraden
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Re: 2=1

Postby Zaraden » Fri Nov 02, 2007 4:58 am UTC

Crap....

Sorry guys, I hate to have reposted it.... I did try searching, but yeah it requires three characters. I'm new, forgive me.
Last edited by Zaraden on Fri Nov 02, 2007 5:02 am UTC, edited 1 time in total.
Let epsilon be less than zero...

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Mathmagic
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Re: 2=1

Postby Mathmagic » Fri Nov 02, 2007 5:02 am UTC

Zaraden wrote:Crap....

Sorry guys, I hate to have reposted it.... I did try searching, but yeah it requires three characters.

No worries! :smile: At least you made the effort.
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3.14159265...
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Re: 2=1

Postby 3.14159265... » Fri Nov 02, 2007 5:51 am UTC

Some in another forum once showed the following paradox:

0.9999..... = 1 :roll:
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Torn Apart By Dingos
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Re: 2=1

Postby Torn Apart By Dingos » Fri Nov 02, 2007 9:03 am UTC

3.14159265... wrote:Some in another forum once showed the following paradox:

0.9999..... = 1 :roll:


However, 0.124 999 999 999 999 999 999 999 999 999 999 999 999 999... < 0.125. See for yourself.

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MartianInvader
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Re: 2=1

Postby MartianInvader » Fri Nov 02, 2007 2:20 pm UTC

Not sure if it's been done before so I'll just tack it onto this thread:

16 - 36 = 25 - 45----------------------------(Both are -20)
16 - 36 + 81/4 = 25 - 45 + 81/4----------(add 81/4 to each side)
(4 - 9/2)^2 = (5 - 9/2)^2------------------(simplify the x^2 + 2xy + y^2 expressions)
4 - 9/2 = 5 - 9/2 ----------------------------(square root both sides)
=> 4=5

The trick isn't too tough to see, but I still like this one better than the divide-by-zero proofs.
Let's have a fervent argument, mostly over semantics, where we all claim the burden of proof is on the other side!

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Re: 2=1

Postby Dongorath » Fri Nov 02, 2007 2:48 pm UTC

Spoiler:
(4-9/2)^2 = (5 - 9/2)^2 => |4-9/2| = |5-9/2|

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Mathmagic
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Re: 2=1

Postby Mathmagic » Fri Nov 02, 2007 3:43 pm UTC

MartianInvader wrote:Not sure if it's been done before so I'll just tack it onto this thread:

16 - 36 = 25 - 45----------------------------(Both are -20)
16 - 36 + 81/4 = 25 - 45 + 81/4----------(add 81/4 to each side)
(4 - 9/2)^2 = (5 - 9/2)^2------------------(simplify the x^2 + 2xy + y^2 expressions)
4 - 9/2 = 5 - 9/2 ----------------------------(square root both sides)
=> 4=5

The trick isn't too tough to see, but I still like this one better than the divide-by-zero proofs.

Guys... did you not see the link I posted, directing you to a thread that is *filled* with these "proofs", and I'm quite positive that this one has been posted in there too.

Are there ever any mods that come into this here maths forum?
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Buttons
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Re: 2=1

Postby Buttons » Fri Nov 02, 2007 4:27 pm UTC

mathmagic wrote:Guys... did you not see the link I posted, directing you to a thread that is *filled* with these "proofs", and I'm quite positive that this one has been posted in there too.

You're correct, but it's hardly easy to search for. The post in question used the same technique to show 3 = pi, which you're unlikely to spot if you're searching for "4 = 5" or the like.


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