Is 2 ≠ 1, or is it?
Assuming that a = b, we can construct an equation such that it seems as if it proves 2 = 1.
a = b
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a 2 = b × a
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a 2 − b 2 = b a − b 2
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( a − b ) ( a + b ) = b ( a − b )
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( a − b ) ( a − b ) ( a + b ) = ( a − b ) b ( a − b )
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a + b = b
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2 b = b
Where is the flaw in logic (mistake), if there is one?
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1 solution
You should mention the number for each line. P.S. I love the fourth option haha!
Yeah. Maybe I should. Thanks for the idea!
Good Work Keep it up.. :)
Wait. Aren't there mistakes in the fourth, fifth and the last line?
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What do you mean? Where's the mistake?
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a+b doesn't equal b
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@B D – That's the reality of the 4th line
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@A Former Brilliant Member – Isn't a+b=b on the fifth line?
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@B D – The result of the 4th line. Check it again
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@A Former Brilliant Member – I think I got the logic.
@A Former Brilliant Member – Because you can't divide by 0 everything and it is like more important.
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@B D – Yes. That is why the other lines are wrong too.
The reason the flaw is in the fourth line is because a = b , and as a − b = 0 , the equation changes to: 0 ( a − b ) ( a + b ) = 0 b ( a − b ) The mistake then arises there, because as we all know...