How can this (math) be?

tw · 09-23-2006, 05:57 PM

How can this be?

Assume that:
a = b
Therefore:
a^2 = ab
a^2 - b^2 = ab - b^2
(a+b)(a-b) = b (a-b)
a+b = b
Since a = b then
2*b = b
2 = 1

The riddle (a mathematical joke) was provided by EE Times. Yes, a simple algebraic flaw exists. But what is it?

vrai_rennx · 09-23-2006, 06:04 PM

This is totally going to bug the crap out of me until I figure it out... But I worked it out and I can't find the mistake... Ah, my math teachers sucked.

Beestie · 09-23-2006, 06:27 PM

Quote:

Originally Posted by tw

a^2 - b^2 = ab - b^2

a^2 - b^2 = 0. Game over.

Happy Monkey · 09-23-2006, 06:55 PM

Not quite - the problem is that (a-b) is zero, and you are dividing by it in step 3 to 4.

Beestie · 09-23-2006, 09:36 PM

Quote:

Originally Posted by Happy Monkey

Not quite - the problem is that (a-b) is zero, and you are dividing by it in step 3 to 4.

If a = b then a^2 - b^2 = ab - b^2 is the same thing as saying 0 = 0. I think you are done at that point.

Happy Monkey · 09-24-2006, 12:41 PM

Quote:

Originally Posted by Beestie

If a = b then a^2 - b^2 = ab - b^2 is the same thing as saying 0 = 0. I think you are done at that point.

No. 0=0 is OK, just like 1=1 is OK in step one. You just can't divide by zero.

glatt · 09-23-2006, 09:28 PM

Quote:

Originally Posted by tw

(a+b)(a-b) = b (a-b)
a+b = b

To get from (a+b)(a-b) = b (a-b)
to
a+b = b
you must divide each side by (a-b). That's great, except...

since a=b, then (a-b) = (a-a) = 0

Only Chuck Norris can divide by zero.

tw · 09-24-2006, 04:58 PM

Quote:

Originally Posted by glatt

since a=b, then (a-b) = (a-a) = 0

It is called the trivial solution.
a * c = b * c
has a unique solution (for real numbers) EXCEPT when c = 0. We tend to forget the other part of that algebraic relationship: that c cannot equal 0. Once c becomes zero, then any number can equal any other.

Naive will then proclaim that math can be manipulated - another interpretation of "lie, damn lies, and statistics". Instead, by providing only a half fact (by forgetting the part where c cannot equal zero), then a mistake occurs.

c=0 is called the trivial solution; an overlooked mathematical error that glatt has successfully identifed.

glatt · 09-25-2006, 10:30 AM

Quote:

Originally Posted by tw

an overlooked mathematical error that glatt has successfully identifed.

To be fair, Happy Monkey beat me to it. I just didn't see his solution because he hid it behind a white font color. It wasn't until Beestie quoted him later that I saw his entire post.

lumberjim · 09-23-2006, 10:21 PM

i contemplated just posting 'pull my finger' here, but instead, my curiosity has me. .....

what does '^' mean in math?

Beestie · 09-23-2006, 10:33 PM

^ means raise to the power of. So a^2 means a squared and a^3 means a*a*a.

lumberjim · 09-23-2006, 10:43 PM

thank you. now.....pull my finger

mbpark · 09-23-2006, 11:28 PM

Doesn't anyone remember FOIL?

(a+b)(a-b) = b (a-b)
a^2 -ab + ab -b^b
a^2 - b^2
0

Therefore, 2 does not equal 1

9th Engineer · 09-23-2006, 11:36 PM

RIght, the whole thing hinges on one '0=0' set after another. They sneak in a '2*0=0' and try to equate it with 2*1=1, the mistake is in the very last operation.

wolf · 09-24-2006, 02:29 AM

You divide by zero to get from step three to four, don't you?

My junior high Algebra teacher showed us this.

09-23-2006, 05:57 PM	#1
tw Read? I only know how to write. Join Date: Jan 2001 Posts: 11,933	How can this (math) be? How can this be? Assume that: a = b Therefore: a^2 = ab a^2 - b^2 = ab - b^2 (a+b)(a-b) = b (a-b) a+b = b Since a = b then 2*b = b 2 = 1 The riddle (a mathematical joke) was provided by EE Times. Yes, a simple algebraic flaw exists. But what is it?

09-23-2006, 06:04 PM	#2
vrai_rennx Voix de Vérité Join Date: Sep 2006 Location: at the bottom of the sea Posts: 59	This is totally going to bug the crap out of me until I figure it out... But I worked it out and I can't find the mistake... Ah, my math teachers sucked. __________________ ~les beaux esprits se rencontrent~

09-23-2006, 06:55 PM	#4
Happy Monkey I think this line's mostly filler. Join Date: Jan 2003 Location: DC Posts: 13,575	Not quite - the problem is that (a-b) is zero, and you are dividing by it in step 3 to 4. __________________ _________________ \|...............\| We live in the nick of times. \| Len 17, Wid 3 \| \|_______________\| [pics]

09-23-2006, 10:21 PM	#10
lumberjim I can hear my ears Join Date: Oct 2003 Posts: 25,571	i contemplated just posting 'pull my finger' here, but instead, my curiosity has me. ..... what does '^' mean in math? __________________ This body holding me reminds me of my own mortality Embrace this moment, remember We are eternal, all this pain is an illusion ~MJKeenan

09-23-2006, 10:33 PM	#11
Beestie -◊\|≡·∙■·∙≡\|◊- Join Date: Feb 2003 Location: Parts unknown. Posts: 4,081	^ means raise to the power of. So a^2 means a squared and a^3 means aaa. __________________ ♠ ♥ ♣ ♦

09-23-2006, 10:43 PM	#12
lumberjim I can hear my ears Join Date: Oct 2003 Posts: 25,571	thank you. now.....pull my finger __________________ This body holding me reminds me of my own mortality Embrace this moment, remember We are eternal, all this pain is an illusion ~MJKeenan

09-23-2006, 11:28 PM	#13
mbpark Lecturer Join Date: Jan 2001 Location: Carmel, Indiana Posts: 761	Algebra 1 Doesn't anyone remember FOIL? (a+b)(a-b) = b (a-b) a^2 -ab + ab -b^b a^2 - b^2 0 Therefore, 2 does not equal 1

09-23-2006, 11:36 PM	#14
9th Engineer Bioengineer and aspiring lawer Join Date: Apr 2006 Location: Pittsburgh Posts: 872	RIght, the whole thing hinges on one '0=0' set after another. They sneak in a '20=0' and try to equate it with 21=1, the mistake is in the very last operation. __________________ The most valuable renewable resource is stupidity.

09-24-2006, 02:29 AM	#15
wolf lobber of scimitars Join Date: Jul 2001 Location: Phila Burbs Posts: 20,774	You divide by zero to get from step three to four, don't you? My junior high Algebra teacher showed us this. __________________ wolf eht htiw og "Conspiracies are the norm, not the exception." --G. Edward Griffin The Creature from Jekyll Island High Priestess of the Church of the Whale Penis

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