Half the posts over here are trying 2 prove that 1=2 or 0=-1 or

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The discussion centers on a mathematical manipulation that attempts to show that 1 equals 2 or 0 equals -1, highlighting a common fallacy in algebra. The argument begins with the assumption that two real numbers, a and b, are equal, leading to the equation (a-b)(a+b)=b(a-b). The critical mistake occurs when both sides are divided by (a-b), which equals zero, making the division undefined. Participants emphasize that dividing by zero is a fundamental error in mathematics, ultimately revealing the flaw in the initial argument. The discussion serves as a reminder of the importance of careful mathematical reasoning.
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half the posts over here are trying 2 prove that 1=2 or 0=-1 or sumthing like that lol so i thought ill try sumthing of that sort too...its silly...but it fascinated me when i was in class 8.

Let a = b where a, b are any 2 real numbers
a^2 = ab
a^2-b^2=ab-b^2
(a-b)(a+b)=b(a-b)
a+b=b
But a = b therefore b = 2b for any real number b

enjoy! don't curse me for wasting ur time when u find the mistae!
 
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...or a=0...
 
a+b=b;
a=b;
so b+b=b
so b=a=0?
 
Answer in white:

"(a-b)(a+b)=b(a-b)"
a-b=0, so it is meaningless to divide both sides by (a-b)
 
Let a = b where a, b are any 2 real numbers

a2 = ab
Subtract both sides with b2 ==> a2-b2 = ab-b2
Simplify ==> (a-b)(a+b)=b(a-b)
divide with (a-b) ==> a+b = b
a=b gives ==> 2b = b

And the error is as said very simple.
 
toocool_sashi said:
(1) (a-b)(a+b)=b(a-b)
(2) a+b=b

to get eq. (2) from eq. (1)

you have to divide both sides by (a-b)
since a=b
therefore, (a-b)=0...

in addition, you have divided two sides by zero...

a number divided by zero is undefined in math...

got ya!
 
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