how can 2 = 0?

<p>Proof 2 = 0?</p>

<p>2x+2x+2 = 0
2(x+x+1) = 0
2x+1 = 0
2 = 0</p>

<p>I thought of this when I was deriving -b/2a for max/min point of a quadratic function. I know it definately is not correct as 2 cannot be equal to zero. Can someone explain this to me?</p>

<p>2x+1 = 0
2x = -1
x = -1/2</p>

<p>you can't just make the x and 1 disappear</p>

<p>ohhh yeah. I forgot, that zero law thing doesn't always have to apply to both factors. Like 2x=0 doesn't mean 2 also = 0, just x.</p>

<p>i would seriously consider you to restudy algebra I.</p>

<p>Hahaha! But there IS a way to make it so 2 = 1. I just can't remember the proof right now.</p>

<p>shouldnt it be urge?</p>

<p>no, it's one of those trick proofs, i had to learn trick proofs in Proving the unprovable(course offered at my school)
i had prove 1=2 on my first diagonastic test</p>

<p>Yea, but when you prove 1=2 you find that somewhere you used an illegit law or something.</p>

<p>wait, u r talking about normal algebra, in Boolean algebra, things stir the common sense</p>

<p>yep.. it involves dividing by zero, which we know is not allowed, but it oftentimes slips by people</p>

<pre><code> Let us define two variables, a and b such that:
</code></pre>

<p>a = b</p>

<p>Now, multiply both sides by a:
a^2 = ab</p>

<p>Subtract b^2 from both sides:
a^2 - b^2 = ab - b^2</p>

<p>Factor the left side of the equation:
(a + b)(a - b) = ab - b^2</p>

<p>Factor the right side of the equation:
(a + b)(a - b) = b(a - b)</p>

<p>Cancel similar term (a - b) on both sides of the equation:
a + b = b</p>

<p>Since we defined variables a and b to be equal, substitute b for a on the left side:
b + b = b</p>

<p>Condense:
2b = 1b</p>

<p>Cancel similar term b on both sides of the equation:
2 = 1</p>

<p>Whoa! That's funky! I like that, killaerone. Thanks</p>

<p>"i would seriously consider you to restudy algebra I."</p>

<p>-- and i would seriously recommend that you restudy the english language</p>

<p>^^^^ Aren't you the guy who made a thread asking how to make smilies?</p>

<p>:) funny...</p>

<p>The flaw in the "proof" that 2 = 1, of course, is that you cannot cancel by (a-b), since it is 0.</p>

<p>nope, that was iwantfood.</p>

<p>however, i did reply to his post. hehe.</p>

<p>killaerone
i dont think that you can make a+b=b into b+b=b because (a) would have to equal zero so there is your flaw in your arithmetic
consider this on though:
If a = b = 1........ </p>

<pre><code> a^2 - b^2 = a^2 - b^2

(a - b) (a + b) = aa - bb factoring and property of squares

(a - b) (a + b) = aa - ab substitution

(a - b) (a + b) = a (a - b) factoring

         (a + b)  =  a                                   cancellation

            a + a  = a                                    substitution

           1 + 1  =  1                                    substitution

                 2   =  1                                   addition

</code></pre>

<p>Umm, turning a+b=b into b+b=b is exactly the same as your turning a+b=a into a+a=a.</p>

<p>glad that there are some experts on the thread! bravo!</p>

<p>Here are proofs and explanations of their fallacies: <a href="http://en.wikipedia.org/wiki/2%3D1%5B/url%5D"&gt;http://en.wikipedia.org/wiki/2%3D1&lt;/a&gt;&lt;/p>