Mar 30th, 2007, 03:24 AM
Well he says that 6 / Waffles = Something.
Allow us to let something = x.
We now have 6 / Waffles = x, We can now solve for waffles algebraically.
(6/Waffles)*Waffles = xWaffles
6 = xWaffles
Waffles = 6/x
We now know that Something (x) is not zero (You cannot divaide by 0), and not 6, scince Waffles = 6/6 = 1
And there is no such thing as 1 Waffles, Waffles is plural.
So we now have :
Waffles = 6/x {x ≠ 6 or 0}
And assuming we cannot have negative waffles (As negative waffles would require negative waffle matter/batter, or owing of waffles to another, which fortunatly for us, waffles are non tradable, refundable, or legal tender in any country.) We can say that x must be > 0 and not 6.
We now have:
Waffles = 6/x, {x > 0, x ≠ 6}
So if we go back, we now see that "something"≠ anything 0 or less, or 6, if we are dealing with Waffles plural.
Now if we say "you can't get something from nothing" (nothing being understood as 0) We now can see that Something (or 6/waffles) cannot be 0.
So we could NOW say
6/Waffles = x, {x ≠ 0}
This isn't a problem because there is no value for waffles that allows x to be 0.
Heres were waffulus gets interesting.
Im going to take the derivitive of Waffles (Waffles = x*waffle) And still this is true, for there to be plural waffle, or waffles, the restrictions on x still apply (x>0 and x≠6) We find out you cannot have 6 waffle because of the identity
Waffles = 6/x
If we substitute the dirivitive of Waffles (x*Waffle) into the equation we get
x Waffle = 6/x
Now if we substitute 6 into something we get
6 Waffles = 6/6
6 Waffles = 1
Last time I checked 6 Waffles does not equal one. Moving on. If we grab our Derivitive Waffle Equation (x Waffle = 6/x) and solve for x (something)
xWaffle = 6/x
(xWaffle)/x = (6/x)/x
Waffle = 6/(x^2)
Waffle(x^2) = (6/(x^2))(x^2)
(x^2)Waffle/Waffle = 6/Waffle
x^2 = 6/waffle
x = √(6/waffle)
You guys need a breather after that? so we now have 3 crutial equations, the Derivitive Waffle Equation (x = √(6/waffle)) and the General Waffles equation (Waffles = 6/x) and the General Something Equation (x = 6/Waffles)
Something interesting comes up, 2 of our equations equal x, therefore we shall make them equal to eachother.
x = 6/Waffles = √(6/waffle)
(6/Waffles)^2 = (√(6/waffle))^2
36/Waffles^2 = 6/waffle
-cross multiply-
6 waffle = Waffles ^2
Waffles = √6 waffle
And now if we substitute the derivitive of Waffles (x*waffle)
x waffle = √(6 waffle)
x^2 waffle^2 =6 waffle
x^2 = 6waffle/waffle^2
x^2 = 6/waffle
x = √(6/waffle) and\or waffle = (6/(x^2))
Recap (Dropping the restrictions for now)
Main Waffles Equation:
Waffles = 6/x
Derived Waffles Eqation:
Waffles = √(6 waffle)
Dervied Waffle Equation:
Waffle = 6/(x^2)
Now If we do some intense substitution we get:
6/x = √6(6/(x^2))
Square both sides
36/(x^2) = 6(6/(x^2)
Divide by 6
36/(6(x^2) = 6/(x^2)
And there we have it
6/(x^2) = 6/(x^2)
1=1
Turns out Waffle Math makes a load of sence. Just really turns out that something can't be negative or 6 when dealing with Waffles. But yeah, you can have 6 waffle and still have syrup.
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