I Broke Mathematics

MarkFL

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$\begin{array}{rcl}a & = & b \\ a+a & = & a+b \\ 2a & = & a+b \\ 2a-2b & = & a+b-2b \\ 2(a-b) & = & a-b \\ 2 & = & 1 \end{array}$

Where did I go wrong?
 
psalms 91

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lol I love it
 
Lamb

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Ephesians 5:31

For this reason a man shall leave his father and mother and shall be joined to his wife, and the two shall become one flesh.

So 2 = 1 is correct :)
 
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MarkFL said:
$\begin{array}{rcl}a & = & b \\ a+a & = & a+b \\ 2a & = & a+b \\ 2a-2b & = & a+b-2b \\ 2(a-b) & = & a-b \\ 2 & = & 1 \end{array}$

Where did I go wrong?
Click to expand...

Care to explain your final step? There's no logic in it.
 
Ruth

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Lämmchen said:
Ephesians 5:31

For this reason a man shall leave his father and mother and shall be joined to his wife, and the two shall become one flesh.

So 2 = 1 is correct :)
Click to expand...

How does that answer the op?
 
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MarkFL said:
$\begin{array}{rcl}a & = & b \\ a+a & = & a+b \\ 2a & = & a+b \\ 2a-2b & = & a+b-2b \\ 2(a-b) & = & a-b \\ 2 & = & 1 \end{array}$

Where did I go wrong?
Click to expand...

In the last step; 2*0 = 1*0 is correct but that does not mean 2 = 1 :p
 
MarkFL

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MoreCoffee said:
In the last step; 2*0 = 1*0 is correct but that does not mean 2 = 1 :p
Click to expand...

Yes, you correctly spotted the error...if $a=b$ then $a-b=0$ and in my last step I divided by zero (a mathematical no-no) to obtain the erroneous result.

Well done! :music:
 
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Ruth said:
How does that answer the op?
Click to expand...

I knew the answer was wrong but sometimes wrong answers aren't always what they appear to be. Hence the quote from scripture ;)
 
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MarkFL said:
Yes, you correctly spotted the error...if $a=b$ then $a-b=0$ and in my last step I divided by zero (a mathematical no-no) to obtain the erroneous result.

Well done! :music:
Click to expand...

Not very well done; I have degrees in pure mathematics :p
 
MarkFL

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MoreCoffee said:
Not very well done; I have degrees in pure mathematics :p
Click to expand...

Well, that certainly gave you an advantage, but no one can fault you for using that here. :)
 
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MarkFL said:
Well, that certainly gave you an advantage, but no one can fault you for using that here. :)
Click to expand...

While at university, as an amusement for myself, I created a proof that 3 = 1 using a quadratic equation. How about you try the same, it is not so hard :)
 
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