Proof: Suppose that a=b. Then
a = b
a^2 = ab
a^2 - b^2 = ab - b^2
(a + b )(a - b ) = b(a - b )
a + b = b
a = 0
However:
If a + b = b, and a = b,
Then
b + b = b, and 2b = b,
Therefore
2 = 1
Full Version: Math Problem
Theorem : All numbers are equal to zero.
Proof: Suppose that a=b. Then
a = b
a^2 = ab
a^2 - b^2 = ab - b^2
(a + b )(a - b ) = b(a - b )
a + b = b
a = 0
However:
If a + b = b, and a = b,
Then
b + b = b, and 2b = b,
Therefore
2 = 1
Proof: Suppose that a=b. Then
a = b
a^2 = ab
a^2 - b^2 = ab - b^2
(a + b )(a - b ) = b(a - b )
a + b = b
a = 0
However:
If a + b = b, and a = b,
Then
b + b = b, and 2b = b,
Therefore
2 = 1
WOW!!!!!!!! 
im dizzzy.lol
im dizzzy.lol
I don't think I understood any of that, but I'm going to show this to my dad. He's damn good at maths. I bet he'll like this.
Well, if b=0,
and 2b=b
therefore b=0.
Anything times zero is zero. One the left side, 0x2=0, and we established b=0, so I'm not sure why it said 2=1.
Advanced algebra has never been my strong suit, so if I've messed something up here, do tell.
and 2b=b
therefore b=0.
Anything times zero is zero. One the left side, 0x2=0, and we established b=0, so I'm not sure why it said 2=1.
Advanced algebra has never been my strong suit, so if I've messed something up here, do tell.
| QUOTE |
(a + b )(a - b ) = b(a - b ) a + b = b |
You simplified by (a-b ) but (a-b )=0 (because a=b ), that's were the problem is in your demonstration.
It's no valid to simplify by 0 because 0*x = 0*y.
TheLight
I struggle with basic maths, so I doubt that I can. 
| QUOTE (babyforrest @ Nov 25 2003, 06:31 PM) |
| I'm not sure why it said 2=1. |
The 2=1 was an argument against the first statement.
| QUOTE (TheLight @ Nov 25 2003, 09:41 PM) |
| You simplified by (a-b ) but (a-b )=0 (because a=b ), that's were the problem is in your demonstration. |
Actually, (a-b )=(a-b ), regardless if it is 0. It still cancels out.
| QUOTE |
| It's no valid to simplify by 0 because 0*x = 0*y. |
(It is also very rude to introduce extra variables when they were not invited
)
| QUOTE |
| schadeaux Posted on Nov 20 2003, 07:14 PM Theorem : All numbers are equal to zero |
All numbers cannot equal zero, only zero equals zero and all numbers are themselves.
2b means (2xb) and as babyforrest said
| QUOTE |
| Anything times zero is zero |
so 2=1 is false, 2=2 and 1=1
b+b (0+0) = b = 0
and
(2xb(0)) = b = 0
| QUOTE (Mystic Mog @ Nov 26 2003, 10:28 AM) | ||||
All numbers cannot equal zero, only zero equals zero and all numbers are themselves. 2b means (2xb) and as babyforrest said
so 2=1 is false, 2=2 and 1=1 b+b (0+0) = b = 0 and (2xb(0)) = b = 0 |
That's what I was trying to say! I'm still not sure where the idea of 2=1 comes from. I'm a little better at algebra than I said before!
| QUOTE (schadeaux @ Nov 26 2003, 02:24 PM) | ||
Actually, (a-b )=(a-b ), regardless if it is 0. It still cancels out. |
No it doesn't, it's basic mathematics that you cannot simplify by 0 and I stated why. I know the education system sucks in the US but there's really no excuse for such a mistake.
Here's a more detailed proof that you cannot simplify by 0:
In order to "cancel out" as you say, the operation you perform is multiplying by the inverse. So canceling out by 0 means dividing by 0 which is not possible.
I mean it's not Einstein's general relativity here !!! It's highschool level maths !
TheLight
If we've already proved that a = 0, and we've proved that a = b, then b = 0...the second equation is utterly meaningless...we already know the value of b is zero. You could slot any number you like in front of b...it would always still be equal to a single b (0)
2b=b
2=1
would only be true if the value for b=1...but it's not, it's 0 you just added in a value for it that didn't exist.
2b=b
2=1
would only be true if the value for b=1...but it's not, it's 0
you just added in a value for it that didn't exist.
This has been proved to be an algebraic fallacy CLICK HERE
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