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Mathematical Fallacy
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| Revenge |
Posted on 07/29/2013 12:46:23
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Super Admin
Posts: 1297
Joined: 28.06.12
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So I copied this from thescienceforum.com. Can you identify the mistake? Don't Google the answer.
Theorem: 4 = 5
'Proof':
-20 = -20 (obviously...)
16 - 36 = 25 - 45 (just two different ways to write -20)
4^2 - 9*4 = 5^2 - 9*5 (factoring...)
4^2 - 9*4 + 81/4 = 5^2 - 9*5 + 81/4 (add 81/4 to both sides)
(4 - 9/2)^2 = (5 - 9/2)^2 ("completing the square" )
4 - 9/2 = 5 - 9/2 (get rid of the squares)
4 = 5 (cancel the 9/2 from both sides)
Why is this wrong?
Edited by Revenge on 07/29/2013 12:47:22
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| stunt1man |
Posted on 07/29/2013 14:25:51
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ShawnPeezy
Posts: 2148
Joined: 20.02.12
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because you can't just write -20 = -20 in the first place without any support from the letters? 
Halo PC Stunting Community - Rank-experienced/rcon holder
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| Hotpot |
Posted on 07/29/2013 14:45:14
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Senior Member
Posts: 397
Joined: 25.05.11
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Ask ninja, ill look at it more after work
Which one are you? |
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| weeshuggy |
Posted on 07/29/2013 18:56:53
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Wanker
Posts: 785
Joined: 23.06.11
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I think I have this, follow it through REALLY carefully and you will spot the mistake. The writing is actually what gives it away... Otherwise I think I might of missed it. |
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| za heystarface |
Posted on 07/29/2013 22:42:57
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Admin
Posts: 6130
Joined: 20.11.10
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"completing the square" doesn't make sense to me. I thought that meant taking the square root of. So I get lost there. Ninja gotta get online.
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| Whatmesage |
Posted on 07/30/2013 01:00:57
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Member
Posts: 125
Joined: 08.04.13
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And to think I used to be good at math.....
I think it's the getting rid of the squares part, but I'm lost.
A BUTTERFLY!!!!!!
Sooooooo...... |
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| stunt1man |
Posted on 07/30/2013 01:45:23
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ShawnPeezy
Posts: 2148
Joined: 20.02.12
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he is just using the formula (a-b )^2 = a^2 -2ab + b^2
a^2 = 4^2
b^2 = (9/2)^2
2.a.b = 2 x 4 x (9/2)
Edited by stunt1man on 07/30/2013 01:46:05
Halo PC Stunting Community - Rank-experienced/rcon holder
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| weeshuggy |
Posted on 07/30/2013 04:16:34
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Wanker
Posts: 785
Joined: 23.06.11
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Yeah you cant just get rid of he squares. You would have to take the square rot on either side.... |
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| ninja |
Posted on 07/30/2013 10:52:26
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Super Admin
Posts: 4174
Joined: 15.11.10
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stunt1man wrote:
because you can't just write -20 = -20 in the first place without any support from the letters?
You can write -20 = -20. It's true (just not very interesting!).
za heystarface wrote:
"completing the square" doesn't make sense to me. I thought that meant taking the square root of. So I get lost there. Ninja gotta get online.
Completing the square is a standard technique for simplifying quadratics: you transform something of the form ax^2 + bx + c to something of the form (dx + e)^2 + f. It's useful for solving quadratics (equivalent to the quadratic formula), and for demonstrating positivity, to give a couple of examples.
Whatmesage wrote:
And to think I used to be good at math.....
I think it's the getting rid of the squares part, but I'm lost.
I think so too.
weeshuggy wrote:
Yeah you cant just get rid of he squares. You would have to take the square rot on either side....
Exactly, you can't just 'get rid of the squares' - although the radical sign denotes the positive square root so you'd have to be careful.
a^2 = b^2 does not imply that a = b (although the implication is true the other way round). You can only conclude that a = ±b (positive or negative). [Note that (-x)^2 = x^2]
This becomes evident if you evaluate the expressions within parentheses on the 5th line (4 - 9/2)^2 = (5 - 9/2)^2. You'll notice that it's (-0.5)^2 = (0.5)^2. Clearly this is true since squaring gives an absolute value (rather than a signed value) for real numbers. However, you can't just drop the exponent without worrying about signs since an even exponent produces a positive result for any (including a negative) real base. The correct line 6 should be 4 - 9/2 = - (5 - 9/2), producing no fallacy.
E:
Basically, a similar but less convincing set of statements would be ...
4 = 4
Equivalently, (-2)^2 = 2^2
Hence, -2 = 2
Clear nonsense, but when disguised behind unsimplified expressions the fallacy can be masked.
Edited by ninja on 07/30/2013 12:12:36
My brain is open.
- Paul Erdős |
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| Target |
Posted on 07/30/2013 11:12:43
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Numpty
Posts: 1425
Joined: 19.07.12
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ninja wrote:
stunt1man wrote:
because you can't just write -20 = -20 in the first place without any support from the letters?
You can write -20 = -20. It's true (just not very interesting!).
za heystarface wrote:
"completing the square" doesn't make sense to me. I thought that meant taking the square root of. So I get lost there. Ninja gotta get online.
Completing the square is a standard technique for simplifying quadratics: you transform something of the form ax^2 + bx + c to something of the form (dx + e)^2 + f. It's useful for solving quadratics (equivalent to the quadratic formula), and for demonstrating positivity, to give a couple of examples.
Whatmesage wrote:
And to think I used to be good at math.....
I think it's the getting rid of the squares part, but I'm lost.
I think so too.
weeshuggy wrote:
Yeah you cant just get rid of he squares. You would have to take the square rot on either side....
Exactly, you can't just 'get rid of the squares' - although the radical sign denotes the positive square root so you'd have to be careful.
a^2 = b^2 does not imply that a = b (although the implication is true the other way round). You can only conclude that a = ±b (positive or negative). [Note that (-x)^2 = x^2]
This becomes evident if you evaluate the expressions within parentheses on the 5th line (4 - 9/2)^2 = (5 - 9/2)^2. You'll notice that it's (-0.5)^2 = (0.5)^2. Clearly this is true since squaring gives an absolute value (rather than a signed value) for real numbers. However, you can't just drop the exponent without worrying about signs since an even exponent produces a positive result for any (including a negative) real base. The correct line 6 should be 4 - 9/2 = - (5 - 9/2), producing no fallacy.
Yeah, wut he said? 
/I was told there would be no math..oh wait..
Lasso Lassie's Legendary Legless Lego-Legolas!
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| za heystarface |
Posted on 07/30/2013 14:45:18
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Admin
Posts: 6130
Joined: 20.11.10
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I knew it! *shifty eyes*
BTW, I taught ninja all he knows.
*more shifty eyes*
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| Revenge |
Posted on 07/30/2013 17:02:59
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Super Admin
Posts: 1297
Joined: 28.06.12
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I think Ninja is the smartest person I know, and I don't even know him. Hmm.
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| Saviour |
Posted on 07/30/2013 17:06:47
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Numpty
Posts: 1352
Joined: 05.10.11
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This whole thread looks like gibberish to me... |
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| za heystarface |
Posted on 07/30/2013 17:23:11
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Admin
Posts: 6130
Joined: 20.11.10
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I KNOW he's the smartest person I know.
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| ninja |
Posted on 07/30/2013 18:10:09
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Super Admin
Posts: 4174
Joined: 15.11.10
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Lol you guys <3.
Have you got any more of these Revenge? They're interesting.
My brain is open.
- Paul Erdős |
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| Vulture |
Posted on 07/30/2013 20:55:03
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Newbie
Posts: 0
Joined: 25.08.12
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ZÅ + Ninja = a calculator
^ Problem solved. 
 Proud to be in the Jajaja group! |
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| FC_SlimJim |
Posted on 07/30/2013 21:17:12
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Super Admin
Posts: 4725
Joined: 14.11.10
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ninja wrote:
Lol you guys <3.
Have you got any more of these Revenge? They're interesting.
aye, boring level math |
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| Revenge |
Posted on 07/30/2013 21:40:27
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Super Admin
Posts: 1297
Joined: 28.06.12
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I'm sure with my couple hundred hours experience of internet searching and few hours talking with math teachers I can find something.
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