Im trying to prove to my friend that what he's saying makes no sense. In any case, here's the argument...can someone refute it?
Read:- 'a2' below as "a squared," 'b2' below as "b squared," etc.
If a = b (so I say) [a = b]
And we multiply both sides by a
Then we'll see that a2 [a2 = ab]
When with ab compared
Are the same. Remove b2. OK? [a2-b2 = ab-b2]
Both sides we will factorize. See?
Now each side contains a - b. [(a+b)(a-b) = b(a-b)]
We'll divide through by a
Minus b and olé
a + b = b. Oh whoopee! [a+b = b]
But since I said a = b
b + b = b you'll agree? [b+b = b]
So if b = 1
Then this sum I have done [1+1 = 1]
Proves that 2 = 1. Q.E.D.
good luck I only argued on grounds that he keeps assuming shit hehe but that argument aint good enough..
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Jan-30-2004 05:51
mmilo
Senior tranceaddict
Registered: Dec 2002
Location: Toronto
if a=b,
then a-b=0
and you cannot divide by zero.
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Jan-30-2004 06:03
King_Mack
Professor of Pimpology
Registered: Oct 2002
Location: Toronto, Canada
i took that approach, but he's not too impressed by that hrm...
is there anything else you can see that flaws from what he presented? I mean..from first glance, it seems mathematically correct(his induction)....but theres something in there that doesnt make sens. I cant put my finger on it though, unless the only thign is the division issue..
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Jan-30-2004 06:08
{b.s.e.}
savant garde
Registered: Oct 2001
Location: The Source
I think your problem is right here: Remove b2. OK? [a2-b2 = ab-b2]
I don't even know where b^2 comes from. We have a^2, as well as ab. Even if you had b^2 you cannot subtract that from ab since they are not like terms. I think you need to make substitutions so that your algerbra is suitable. But of course, once you make subs, everything will equal zero and will render your equation void.
I hate math, I'm going to play some chess.
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Jan-30-2004 06:16
Perfect_Cheezit
Machine Beat
Registered: Jul 2003
Location: MNTA #08
just wait for Noisician, he'll set things straight
Jan-30-2004 06:20
_Nut_
North x NorthWest
Registered: Nov 2001
Location: 61.105423,-149.723555
(original eq)
a = b
(both sides mult through by a)
a^2 = ab
When with ab compared
a = b
ab = b^2
Are the same. Remove b2. OK? [a2-b2 = ab-b2]
a^2 = ab = b^2
(division to remove the middle term)
a/b = 0 = b/a
where a/b = -b/a
then
a^2/b = -b
a^2 = -1
therefore
a = sqrt(i) [you cannot take the sqrt of negative nums so you have to bust out the imaginary numbers algebra]
you were coming up with some odd shit. saying things factored and all that. following through the begining this is what i computed. Are you trying make up some theorum of sorts? if you are you need to lay off the green.
Jan-30-2004 06:22
DasBrotBesser
Senior tranceaddict
Registered: Apr 2003
Location: DC!!
you're forgetting that ab=a^2=b^2 since a=b
hence it should be a^2=ab=B^2
remove b^2
therefore a^2-b^2=b^2-b^2=0
but even without that, a-b=0, so then it would be
(a+b)(0)=b(0)=0
so then your last equation would be 0=0
Jan-30-2004 06:40
DrUg_Tit0
e^(i*pi)+1=0
Registered: Nov 2002
Location: Zagreb, Croatia
Re: A Weird Math Problem ....
quote:
Originally posted by King_Mack
Now each side contains a - b. [(a+b)(a-b) = b(a-b)]
We'll divide through by a
Minus b and olé
As mmilo said earlier, the division by 0 is where the flaw lies. First you have (a+b)*0=b*0=0, and so far the argument is a correct one. But after the division, you basically get (a+b)*0/0=b*0/0 which is not defined because 0/0 can be equal to anything.
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1+1=10
Jan-30-2004 12:12
Flyboy217
Senior tranceaddict
Registered: Aug 2003
Location: In DEEP SPACE... Space... space... sp...
quote:
Originally posted by King_Mack
i took that approach, but he's not too impressed by that hrm...
is there anything else you can see that flaws from what he presented? I mean..from first glance, it seems mathematically correct(his induction)....but theres something in there that doesnt make sens. I cant put my finger on it though, unless the only thign is the division issue..
This explanation is correct. Dividing by zero invalidates the equation. Your friend's "proof" belongs to a whole class of such spurious explanations of false equalities.
Jan-30-2004 22:12
whiskers
old skool
Registered: Sep 2001
Location: in your dreams
Re: Re: A Weird Math Problem ....
quote:
Originally posted by DrUg_Tit0
As mmilo said earlier, the division by 0 is where the flaw lies. First you have (a+b)*0=b*0=0, and so far the argument is a correct one. But after the division, you basically get (a+b)*0/0=b*0/0 which is not defined because 0/0 can be equal to anything.
i confirm that too, there are a bunch of problems in computer & math textbooks that rely on this "division by 0" approach to have you find the error in the algorithm.
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Jan-30-2004 22:30
zarathustra
0x40000000
Registered: Sep 2001
Location: Calgary
Division by zero is illegal.
Jan-31-2004 02:58
astroboy
Supreme tranceaddict
Registered: Nov 2001
Location: Melbourne
quote:
Originally posted by King_Mack
i took that approach, but he's not too impressed by that hrm...
Impressed or not, you simply CAN NOT divide by zero. As soon as he does that his proof becomes invalid.
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