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Subject: "All numbers equal??"     Previous Topic | Next Topic
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Gavin
guest
Aug-12-05, 09:37 AM (EST)
 
"All numbers equal??"
 
   I have recently stumbled upon this on a website and, along with several of my friends, have been trying to figure out if this is indeed valid or if there is a flaw somewheres in the mathmatics of it. Forgive me if it is something trivial for we have just graduated high school and may not have the knowledge needed to figure this out. Any help or explanation would be welcome. Here it is:
<prepared>Theorem: All numbers are equal.
<prepared>Proof: Choose arbitrary a and b, and let t = a + b. Then
<prepared>a + b = t
<prepared>(a + b)(a - b) = t(a - b)
<prepared>a^2 - b^2 = ta - tb
<prepared>a^2 - ta = b^2 - tb
<prepared>a^2 - ta + (t^2)/4 = b^2 - tb + (t^2)/4
<prepared>(a - t/2)^2 = (b - t/2)^2
<prepared>a - t/2 = b - t/2
<prepared>a = b
<prepared>So all numbers are the same, and math is pointless.
(Copied from https://www.bash.org/?522860)


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  Subject     Author     Message Date     ID  
All numbers equal?? Gavin Aug-12-05 TOP
  RE: All numbers equal?? alexb Aug-12-05 1
     RE: All numbers equal?? Gavin Aug-12-05 2
         RE: All numbers equal?? alexb Aug-13-05 3
             RE: All numbers equal?? Gavin Aug-13-05 4
                 RE: All numbers equal?? alexb Aug-14-05 5
                     RE: All numbers equal?? Gavin Aug-14-05 6

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alexb
Charter Member
1620 posts
Aug-12-05, 09:41 AM (EST)
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1. "RE: All numbers equal??"
In response to message #0
 
   >I have recently stumbled upon this on a website and, along
>with several of my friends, have been trying to figure out
>if this is indeed valid or if there is a flaw somewheres in
>the mathmatics of it.

Assume I told you there was no flaw, what would be your reaction?

>Forgive me if it is something trivial
>for we have just graduated high school and may not have the
>knowledge needed to figure this out.

You have all the knowledge you may need to resolve your quandary.

>Any help or
>explanation would be welcome.

Forthcoming upon your response.


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Gavin
guest
Aug-12-05, 07:52 AM (EST)
 
2. "RE: All numbers equal??"
In response to message #1
 
   well, first off, I have no sweet clue what quandary means, so I'll assume it is a made up word. And second off, if there is no flaw, then I'll simply tell people that this is some (**** bad word removed) up ##### and give up on math for the rest of my life... but not really, I'll just think this is something neat to show people.


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alexb
Charter Member
1620 posts
Aug-13-05, 08:04 AM (EST)
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3. "RE: All numbers equal??"
In response to message #2
 
   >well, first off, I have no sweet clue what quandary means,
>so I'll assume it is a made up word.

No, quandary means predicament, difficulty. You can check this online at, e.g., https://www.dictionary.com

>And second off, if
>there is no flaw, then I'll simply tell people that this is
>some (**** bad word removed) up #####

Foul language is not allowed here. Please refrain from using it in the future.

So you do suspect there is a flaw. Good. I quite agree with that. But in this case your original question was poorly formulated. It appeared as if you allowed for a possibility that the argument was correct.

>and give up on math
>for the rest of my life... but not really, I'll just think
>this is something neat to show people.

I strongly believe that more appreciation will be engendered after people try to use thair brains to resolve the question by themselves.
Perhaps checking

https://www.cut-the-knot.org/do_you_know/mul_eq.shtml

will give you a clue.


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Gavin
guest
Aug-13-05, 10:48 PM (EST)
 
4. "RE: All numbers equal??"
In response to message #3
 
   First, I appoligize for the bad language, I should of realized it wouldn't of been appreciated, guess I just wasn't thinking about it at the time. The link you provided did help me relized something, the flaw when the square root of each side was taken it didn't allow for the posibility of the negative root. Or at least I believe that's what the point of the site was, that's what I got from it at least. But I fail to see how this would make a significant difference in the outcome, since for the negative root you would simply end up getting -a=-b which is the same as saying a=b, maybe I'm missing something here too, I'm not sure. Unfortionately I do not have the time now to look further into this line of reasoning since so I'll have to try to figure this out tonight or tomorrow whenever I again have some free time. Thanks for the help so far, any other small pushes along the right line would be appreciated, for as you said, problems are much better appreciated when you solve them yourself, even if you have had some help along the way :).


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alexb
Charter Member
1620 posts
Aug-14-05, 00:08 AM (EST)
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5. "RE: All numbers equal??"
In response to message #4
 
   >But I fail to see how this would make a significant
>difference in the outcome, since for the negative root you
>would simply end up getting -a=-b which is the same as
>saying a=b, maybe I'm missing something here too, I'm not
>sure.

There is another possibility here: a = -b.

For example,

(-5)2 = 25 = 52,

but you would not claim that -5 = 5, right?


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Gavin
guest
Aug-14-05, 09:59 AM (EST)
 
6. "RE: All numbers equal??"
In response to message #5
 
   Yes, I realized your point yesterday while on break at work. And that after you square root both sides getting +/-(a-t/2)=+/-(b-t/2) it's the negative of one side that equals the positive of the other since a and b will be equal amounths greater then and less than t/2 since they equal t. I'm not sure how you would show this in the next step of it though, I've never done questions with 2 +/- when I was in school. I would assume you'd then have 4 posible combinations and you'd somehow show that the two showing that a=b are false and the other two simplify to being a+b=t which is of course what you started with. Thanks for all your help figuring this out, and this just reinforced my hatred of quare rooting :P. Just kidding of course.


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