<p><a href="http://en.wikipedia.org/math/8c261e7ca3ae362c47eafdcecc100a9c.png%5B/url%5D%5B/i%5D">http://en.wikipedia.org/math/8c261e7ca3ae362c47eafdcecc100a9c.png</a></p>
<p>I like Maize&Blue22's post...
you can directly say -</p>
<p>2² = (-2)²
2 = -2</p>
<p>Samwise, I'm asking for summation upto finite 'n'...</p>
<p>Well I went ahead and took the limit as n -> inf :p</p>
<p>yes but no bonus points :p n->inf is easier than finite n</p>
<p>(-2)²=2</p>
<p>...</p>
<p>-20 = -20
16 - 36 = 25 - 45
4^2 - 9<em>4 = 5^2 - 9</em>5
4^2 - 9<em>4 + 81/4 = 5^2 - 9</em>5 + 81/4
(4 - 9/2)^2 = (5 - 9/2)^2
4 - 9/2 = 5 - 9/2 <-- This step is not correct. When going from a^2 = b^2 to a = b, one must check afterward for the possibility that a = -b, which is the case here.
4 = 5</p>
<p>I didnt understand Knavish' post.. :confused:</p>
<p>Try this:
1-1/2+1/3-1/4+1/5-1/6...=ln(2)</p>
<p>But then:
(1-1/2-1/4)+(1/3-1/6-1/12)+(1/5-1/10-1/20)...=0+0+0...=0</p>
<p>So ln(2)=0?</p>
<p>:confused:
Godforsaken thread.....
Either I am dumb or you are..
How in samcrap is (1 - 1/2 - 1/4) + (1/3 - 1/6 - 1/12) .. = 0 + 0.. ??</p>
<p>Proof that 1=2</p>
<p>1=a
2=b
a=b</p>
<p>more like</p>
<p>a=1
b=2
!(a=b) <-- true</p>
<p>Oh crap...I forgot some dots...should read:
(1-1/2-1/4...)+(1/3-1/6-1/12...)+(1/5-1/10-1/20...)...=0+0+0...=0</p>
<p>Meaning you keep subtracting, like the first part would be (1-1/2-1/4-1/8-1/16-1/32...)</p>
<p>"1=a
2=b
a=b"</p>
<p>Ok... you can set a variable to equal a number (i.e. a = 1), but you cant set a number equal to a variable. Even if you could... it would go something like this:</p>
<p>1=a (a is 1)
2=b (b is 2)
a=b (a and b are both 2)</p>
<p>2=2</p>
<p>Wow!</p>
<p>:)</p>
<p>HiWei that is only assuming that it is sequential and not simultaneous</p>
<p>How about this:</p>
<p>∞=∞</p>
<p>(1+2+3+4...)=∞
2<em>(1+2+3+4....)=2</em>∞=(2+4+6+8...)
(2+4+6+8...)=∞
∞=2<em>∞
1</em>∞/∞=2*∞/∞
1=2</p>
<p>:D</p>
<p>i would seriously reccomend that you guys get a life.</p>
<p>videogamer- That would make a mathematician proud ;)</p>
<p>How about this:</p>
<p>0=2</p>
<p>Q.E.D.</p>
<p>Q.E.D.... Work?</p>
<p>Heh, JK, I know what that is.</p>
<p>videogamer, infinite does not get 2x bigger if you multiply it by 2. </p>
<p>infinite x 2 = infinite</p>
<p>More basic is the fact that you can't just plug in infinity as if it's a number. It isn't a number. We can take the limit as a variable goes to infinity, etc. but you can't just plug in infinity as a number. If a series diverges we use the notation ∞, but it's not like that series is equal to some number.</p>
<p>(1-1/2-1/4...)+(1/3-1/6-1/12...)+(1/5-1/10-1/20...)...=0+0+0...=0</p>
<p>According to that logic, for every positive term, there is an infinite amount of negative terms.</p>
<p>However, the expansion of ln(2) contains an equal number of positive and negative terms.</p>
<p>What I never really got, though...
[IMPORTANT INFORMATION IN BINARY] XOR [RANDOM JUNK] = [MORE RANDOM JUNK]</p>
<p>and</p>
<p>[RANDOM JUNK] XOR [MORE RANDOM JUNK] = [IMPORTANT INFORMATION IN BINARY]</p>
<p>violation of the conservation of information???</p>