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gib wrote:Can anyone spot the trick?
barbarianhorde wrote:(a + b)(a - b) = b(a - b)
a and b are both 0.
Meno_ wrote:Gib, I don't think that's a trick.
gib wrote:Meno_ wrote:Gib, I don't think that's a trick.
What do you mean, Meno_?
gib wrote:Oh, you mean 'trick' as in a form of deception, something that once unveiled removes the magic. I see. In that case, I agree that 1 = 0.999... is not a trick, it's just a fact. And I agree that its standing as a trick will forever be debated by the infinitesimalists. Still, I'm sick of debating it. I want something new, something to ponder my brains over.
You got anything?
Carleas wrote:barbarianhorde wrote:(a + b)(a - b) = b(a - b)
a and b are both 0.
I agree the trick is around this line, but can you explain why this entails that a and b are both 0?
I see the trick as being the move between these two lines:
(a + b)(a - b) = b(a - b)
a + b = b
(a-b) equals zero, so this step requires dividing by zero, which is undefined.
barbarianhorde wrote:Well yes the step only makes sense if both are zero. I didn't win?
barbarianhorde wrote:It doesn't follow unless you said that a is not zero.
gib wrote:Suppose that a = b... then:
(a + b)(a - b) = b(a - b)
a + b = b
lordoflight wrote:It does not follow.
a+b!=(a + b)(a - b)
b(a - b)!= b
gib wrote:lordoflight wrote:It does not follow.
a+b!=(a + b)(a - b)
b(a - b)!= b
You're right, but where in the steps did it say:
a + b = (a + b)(a - b)
b(a - b) = b
lordoflight wrote:You wrote a + b = b Yep, and that (a + b)(a - b)=b(a - b) Yep, that a+b=(a + b)(a - b) Nope, that a +b = b. Yep
gib wrote:lordoflight wrote:You wrote a + b = b Yep, and that (a + b)(a - b)=b(a - b) Yep, that a+b=(a + b)(a - b) Nope, that a +b = b. Yep
lordoflight wrote:You said (a + b)(a - b) = b(a - b). Yep. You said b(a-b)=b. Nope... geez, you aren't very good at this. But it doesn't. Can't. Unless b is zero. D'uh!
lordoflight wrote:There is no "trick" being used here. The original post just doesn't make sense to begin with.
lordoflight wrote:Here is where you said b=b(a-b)
"(a + b)(a - b) = b(a - b)
a + b = b"
You dropped the b down underneath b(a-b). Implying it is the same.
lordoflight wrote:Okay, looking at it further, you put
(a + b)(a - b) = b(a - b)
Which does not follow.
It would produce nonsensical results such as this:
(3+4)(3-4)=4(3-4)
-7=-4
gib wrote:Suppose that a = b...
gib wrote:I'm interested in this:
1 + 2 + 3 + 4 + 5 + 6 + 7 + .... = -1/12
lordoflight wrote:Okay, looking at it further, you put
(a + b)(a - b) = b(a - b)
Which does not follow.
lordoflight wrote:It would produce nonsensical results such as this:
(3+4)(3-4)=4(3-4)
-7=-4
lordoflight wrote:The crux of what you are doing, is exposing a flaw in mathematics. You set the value of the equations to zero, so it erodes any qualities the equations originally had.
See my thread called "the number delusion".
lordoflight wrote:The same thing happens when you scale a 3 dimensional shape to zero. You can scale it to 10%, 50%, or even a negative, and still retain the shape. But once you set it to zero information is lost and the shape no longer exists. That is the crux of what you are doing here.
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