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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 !!! 

[mmijares]

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.

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]

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

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 

[Astrapho]

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

[mmijares]

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

Hi Astrapho,

Since x = y, the above division is a division by zero.  In ordinary arithmetic, division by zero is not a legitimate operation.  (Source: http://en.wikipedia.org/wiki/Division_by_zero)

[longhorn]

Sometimes I have been going number 2 and 1 at the same time, so I would say yes... most definitely 2 can equal 1.

Longhorn

[Dave in Tenn]

let h=head.

2h > 1

People shouldn't do math with letters.