Math is dangerous; proof 2=1

[avb3]

Many sailors use calculations for boat ratios, perhaps rigging, or navigation.

So, this should be easy right?

Here's a mathematical proof that appears to show that 2=1. Can you find what's wrong with it.

Let x=y
Then x^2=xy (by multiplying both sides by x)
Then x^2-y^2=xy-y^2 (by subtracting y^2 from both sides)
Then (x+y)(x-y)=y(x-y) (by factoring both sides)
Then x+y=y (by dividing both sides by (x-y))
Then y+y=y (since x=y by the original assumption)
ie. 2y=y
Therefore 2=1 (by dividing both sides by y)

Clearly 2 and 1 are not equal, what mistake was made above?

[deckofficer]

No mistake made if x=0.

[Target9000]

Originally Posted by avb3

Then (x+y)(x-y)=y(x-y) (by factoring both sides)

Since x = y then (x-y) is 0.

[Target9000]

Also... Math is flawless. Humans are dangerous.

[sctpc]

Since x=y, (x-y)=0,So it is not possible to divide any equation by zero.

[boatman61]

Seeing as none of the Maths I do on board involve Algebra...
x-y= Pointless

[sailorboy1]

Originally Posted by boatman61

Seeing as none of the Maths I do on board involve Algebra...
x-y= Pointless

[pressuredrop]

Originally Posted by avb3

Then (x+y)(x-y)=y(x-y) (by factoring both sides)

cant do that...

(x+y)(x-y) = x^2 - y^2.... NOT yx-y^2....


easyyyyy.... next....

[capn_billl]

You broke several rules, 1, misuse of associative rule, 2. divide by zero.