<![CDATA[Math Is Fun Forum / Proof All Numbers are Equal]]> 2020-09-03T07:28:44Z FluxBB http://www.mathisfunforum.com/viewtopic.php?id=25439 <![CDATA[Re: Proof All Numbers are Equal]]> The main trick occurs in step 1, multiplying both sides by a-b. While not wrong, this introduces the bogus solution a=b to the equation, and allows the oversight when taking the square roots to land on that wrong solution.

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http://www.mathisfunforum.com/profile.php?id=222632 2020-09-03T07:28:44Z http://www.mathisfunforum.com/viewtopic.php?pid=414894#p414894
<![CDATA[Re: Proof All Numbers are Equal]]> Yep, that is true. I am just saying that the incantation "Let a, b be arbitrary numbers. Set c = a + b" should be made explicit.

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http://www.mathisfunforum.com/profile.php?id=95904 2020-01-10T16:34:29Z http://www.mathisfunforum.com/viewtopic.php?pid=412123#p412123
<![CDATA[Re: Proof All Numbers are Equal]]> It's ok to say let a and b be any numbers and define c to be a + b.  As c 'cancels' out of the proof you're just left with a = b.  That's the mystery bit.  Except the proof is flawed at the step where square roots are taken.

Bob

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http://www.mathisfunforum.com/profile.php?id=67694 2020-01-10T15:44:04Z http://www.mathisfunforum.com/viewtopic.php?pid=412122#p412122
<![CDATA[Re: Proof All Numbers are Equal]]> I would like to note a different issue. You cannot start a proof by saying "a + b = c". What kind of objects are a, b, c? Do you mean that for every a, for every b, for every c, a + b = c?

For a lot of people, a proof is something that has human value. An arbitrary calculation is not a proof.

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http://www.mathisfunforum.com/profile.php?id=95904 2020-01-08T23:21:39Z http://www.mathisfunforum.com/viewtopic.php?pid=412105#p412105
<![CDATA[Re: Proof All Numbers are Equal]]> Hi Anthony

Nice 'proof'.  When applying a square root you have to remember that two roots are possible.

9 =9 but 3 ≠ -3

To check out any algebra just substitute some numbers to see what is happening.

I chose a = 5; b = 3 and so c = 8.

Here is your 'proof' with those numbers.

8 x 2 = 8 x 2
25 - 9 = 40 - 24
25 - 40 = 9 - 24
25 -40 + 32 = 9 - 24 + 32
(5-4)^2 = (3-4)^2

All so far is correct. But then we have the square root.

(5-4) ≠ (3-4)

But, back to the algebra, if we take a negative root:

a - c/2 = -b + c/2

a + b = c/2 + c/2 = c

Now it's correct but hasn't given anything new.

Bob

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http://www.mathisfunforum.com/profile.php?id=67694 2020-01-06T10:37:50Z http://www.mathisfunforum.com/viewtopic.php?pid=412081#p412081
<![CDATA[Re: Proof All Numbers are Equal]]> Hi,

Let us number the steps:

From (5) to (6), there is a fallacy.
The the step (5) does not necessarily equal (6).
Got it?

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http://www.mathisfunforum.com/profile.php?id=682 2020-01-06T09:34:36Z http://www.mathisfunforum.com/viewtopic.php?pid=412080#p412080
<![CDATA[Proof All Numbers are Equal]]> Let's prove that all numbers are equal.

What went wrong?

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http://www.mathisfunforum.com/profile.php?id=220121 2020-01-06T07:20:21Z http://www.mathisfunforum.com/viewtopic.php?pid=412079#p412079