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For those who are good in algebra.... Is 2 = 1 ??

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mmijares:
Let x = y
Multiply both sides by x, the equation becomes x2 = xy
Subtract both sides by y2, the equation becomes x2 - y2 = xy - y2
Factor both sides, the equation becomes (x + y)(x - y) = y(x - y)
Divide both sides by (x - y), the equation becomes x + y = y

If x = y, then the equation can be written as y + y = y
or 2y = y
or 2 = 1 !!!  8)

mmijares:

--- Quote from: John from Kentucky on May 13, 2010, 12:19:34 PM ---The contradiction is in the first line, x = y.  x can equal x.  And y can equal y.  But two different unknowns cannot equal each other.  It is a contradiction of terms.

--- End quote ---

You have a point but the flaw is not in the first line.  Although two different unknowns, it MAY, it CAN, it is POSSIBLE that the two is equal.

Astrapho:
As far as I know, x can = y. I came across a few questions in my maths papers whose answers are x=y before.

Holy crapxors! There must be a logic error somewhere! D: Let's sub some values:

1-1 = 1-1
(1+1)(1-1) = 1(1-1)

I think I see our problem. D:

Edit: The only real solution is that y=0 . That works. :9

mmijares:

--- Quote from: Astrapho on May 14, 2010, 07:22:25 AM ---Holy crapxors! There must be a logic error somewhere! D: Let's sub some values:

--- End quote ---

Yes, there is!

When I was in my 1st year high...this drove me mad.
The multiplication, the subtraction, the factoring in the above mathematical statements are all logical...but......BUT!......the division is not  ;D

Astrapho:
Okay, this is driving me mad. D; I see nothing wrong with the division?

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