[Math]Proving 2+2 = 0 and other incredible stuff
Update: Well, hawkeye posted a comment, spotting my grave Mistake. Silly me : I've lost more than one Mark in more than one Maths Paper more than once, and yet I make the same mistake. Stupid me:D Thanks hawkeye, for correcting me before I gave that to my Maths Teacher and get spanked:D
No Joke. I got this during a boring Morning before Second Revision English II Exams. So, I've got proof that 2+2 = 0. After trying to find a mistake in this for some 2 hours yesterday night, I'm posting this here. I'm probably wrong, but I can't find out where I am wrong. So, here we go :
(a) 12 = 1
(b) (-1)2 = 1
(c) From (a) and (b), 12 = (-1)2
(d)Therefore, 1 = -1
Reason : If Powers are equal, bases can be equated
(e) Assume 2+2 = x
(f) (2 x 1) + (2 x 1) = x
Reason : Since 2 = 2 x 1
(g) (2 x 1) + (2 x -1) = x
Reason : Since 1 = -1 [From (d)]
(h) 2 + (-2) = x
(i) 2 - 2 = x
(j) 0 = x
(k) Substituting x = 0 in (e),
2 + 2 = 0
So, this is for a specific case. It can be easily Generalized into a generic form :
x + x = 0
Also, from this, you get :
x = -x
Well, the proof also gives a really interesting Corrollary : Every Number is Equal to any other Number!
Assume any Number1 = x
Then, according to Proof above :
x + x = 0
2x = 0 - (1)
Assume any Number2 = y
Then,
y+y = 0
2y = 0 - (2)
So, from (1) and (2),
2x = 2y
Dividing both sides by 2, we get :
x = y
So, any Number is equal to any other Number! Cool, isn't it ? It also has quite nice implications. Like, I owe someone Rs. 1000. Since, according to the proof, I take x = Rs. 1000 and y = Rs. 1. So, since x = y, I can just pay Rs. 1, since It is equal to Rs. 1000! And, if someone owes me Rs. 1, I can just invert the process, and get Rs. 1000, while ofcourse it can backfire and they can pay me Rs.(-)1000, since obviously, Rs.(-)1000 = Rs. 1000 = Rs. 1.
Well, heard of the word Paradox ? I'm feeling it....
Well, it's got more : All Fractions and Divisons equal 1, since the Numerator and the Denominator will be equal! And, they will also equal any number, without constraint, since 1 can be equal to any number!
Man, Maths will be sooooooooooooo much Easier : I can give any value as answer to any questions, and it will be correct! You'll get 100 out of 100 every time! But wait, 100 out of 100 might as well be equal to 0 out of 100, because 0 = 100. Paradox:D
So, where am I wrong ? What part of the proof is wrong ? I sincerely really Don't know, so you've really gotta help me find the fault with this.....
If you're Still with me after this long post, I want your comments...
(a) 12 = 1
(b) (-1)2 = 1
(c) From (a) and (b), 12 = (-1)2
(d)Therefore, 1 = -1
Reason : If Powers are equal, bases can be equated
(e) Assume 2+2 = x
(f) (2 x 1) + (2 x 1) = x
Reason : Since 2 = 2 x 1
(g) (2 x 1) + (2 x -1) = x
Reason : Since 1 = -1 [From (d)]
(h) 2 + (-2) = x
(i) 2 - 2 = x
(j) 0 = x
(k) Substituting x = 0 in (e),
2 + 2 = 0
So, this is for a specific case. It can be easily Generalized into a generic form :
x + x = 0
Also, from this, you get :
x = -x
Well, the proof also gives a really interesting Corrollary : Every Number is Equal to any other Number!
Assume any Number1 = x
Then, according to Proof above :
x + x = 0
2x = 0 - (1)
Assume any Number2 = y
Then,
y+y = 0
2y = 0 - (2)
So, from (1) and (2),
2x = 2y
Dividing both sides by 2, we get :
x = y
So, any Number is equal to any other Number! Cool, isn't it ? It also has quite nice implications. Like, I owe someone Rs. 1000. Since, according to the proof, I take x = Rs. 1000 and y = Rs. 1. So, since x = y, I can just pay Rs. 1, since It is equal to Rs. 1000! And, if someone owes me Rs. 1, I can just invert the process, and get Rs. 1000, while ofcourse it can backfire and they can pay me Rs.(-)1000, since obviously, Rs.(-)1000 = Rs. 1000 = Rs. 1.
Well, heard of the word Paradox ? I'm feeling it....
Well, it's got more : All Fractions and Divisons equal 1, since the Numerator and the Denominator will be equal! And, they will also equal any number, without constraint, since 1 can be equal to any number!
Man, Maths will be sooooooooooooo much Easier : I can give any value as answer to any questions, and it will be correct! You'll get 100 out of 100 every time! But wait, 100 out of 100 might as well be equal to 0 out of 100, because 0 = 100. Paradox:D
So, where am I wrong ? What part of the proof is wrong ? I sincerely really Don't know, so you've really gotta help me find the fault with this.....
If you're Still with me after this long post, I want your comments...
4 Comments:
ur (d) is wrong. ur forgot square root leads to +/- (plus or minus)
(^ indicates raised to the power of)
(x)^2 = (y)^2
therefore: +/-(x) = +/-(y)
Well i was about to say that, but hawkeye has overtaken me.
Self note: I should fire up bloglines more often....
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