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# FFXI <> FFXIVFollow

Jul 01 2009 at 10:22 AM Rating: Excellent
125 posts
For all those who are worried, I'm working on a mathematical proof to show that FFXI is, in fact, not the same as what FFXIV will be.

Ahem:

Prove FFXI <> (Not equal to) FFXIV

First, multiply both sides by FFXI:

FFXI * FFXI = FFXIV * FFXI

FFXI^2 = FFXIV*FFXI

Now, take the squareroot of both sides:

SQRT(FFXI^2)=SQRT(FFXIV*FFXI)

FFXI = SQRT(FFXIV*FFXI)

Now for some more math:

FFXI = SQRT(FF*FF*XIV*XI)

Let XIV = 14
Let XI = 11

FF11 = FF * SQRT(14*11)

FF11 = FF12.41

Floor both sides:

FLOOR(FF11) = FLOOR(FF12.41)

Therefore:
FF11=FF12
FFXI <> FFXIV

I have a similar proof that involves W0W.
Jul 01 2009 at 10:47 AM Rating: Good
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Awesome post! Made me giggle.
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Jul 01 2009 at 10:57 AM Rating: Good
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Edited, Jul 1st 2009 3:17pm by Karelyn
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KUMQUATS
Jul 01 2009 at 11:02 AM Rating: Excellent
180 posts
lol!! That was great, and so not what I was expecting! Rate up! =D
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Jul 01 2009 at 11:04 AM Rating: Good
230 posts
Well, I just rated you up to scholar!
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Jul 01 2009 at 11:11 AM Rating: Excellent
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Nearly coughed out coffee milk through my nose. (つд⊂)ｺﾞｼｺﾞｼ Rate up!
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Jul 01 2009 at 11:38 AM Rating: Excellent
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Callipho wrote:
I have a similar proof that involves W0W.

I assume it just couldn't fit in the margin of your post, right?
Jul 01 2009 at 11:44 AM Rating: Excellent
125 posts
Glad to see I'm not the only one who enjoys math posts! ^^

And no Kat, it gets into some pretty complicated calculus, and I couldn't be bothered to type "Integral" over and over again rather than getting to make a nice squiggly line. It just wouldn't be the same. Maybe I can scan it and link.
Jul 01 2009 at 12:05 PM Rating: Good
1,826 posts
Yes but I think Vawn did some other math in the XI forums proving that at least some things will be exactly the same. Now where was that post....
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Jul 01 2009 at 6:07 PM Rating: Good
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Blame the computer programmer in me, but the not equal to sign is expressed as: !=

FF11 != FF14

... Alright, back to other things. >.>
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Jul 01 2009 at 6:14 PM Rating: Excellent
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Rellek wrote:
Blame the computer programmer in me, but the not equal to sign is expressed as: !=

FF11 != FF14

... Alright, back to other things. >.>

Different context, different syntax.

I personally like =/=
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KUMQUATS
Jul 02 2009 at 4:40 AM Rating: Excellent
125 posts
<> is not equal to in SQL-speak, for us who have to pseudo code every now and then.

Not that anyone cares... but just to clarify :D
Jul 02 2009 at 5:52 AM Rating: Good
711 posts
Callipho wrote:

FFXI * FFXI = FFXIV * FFXI

FFXI^2 = FFXIV*FFXI

Now, take the squareroot of both sides:

SQRT(FFXI^2)=SQRT(FFXIV*FFXI)

FFXI = SQRT(FFXIV*FFXI)

Now for some more math:

FFXI = SQRT(FF*FF*XIV*XI)

Let XIV = 14
Let XI = 11

FF11 = FF * SQRT(14*11)

FF11 = FF12.41

Floor both sides:

FLOOR(FF11) = FLOOR(FF12.41)

Therefore:
FF11=FF12
FFXI <> FFXIV

I have a similar proof that involves W0W.

But but but.....

You stated that...

FFXI * FFXI = FFXIV * FFXI

That basically just proved that FFXI = FFXIV!

Unless you are trying to prove that FF11 = FF12.41 = FF14....

Sorry...couldn't resist >.>
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Jul 02 2009 at 6:19 AM Rating: Excellent
125 posts
It's a proof. Set them equal, make a few substitutions and see if it holds true (and since we already know FF11<>FF12, voila). This is clearly mathematics at its finest.

Edited, Jul 2nd 2009 10:37am by Callipho
Jul 02 2009 at 6:56 AM Rating: Excellent
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Callipho wrote:
It's a proof. Set them equal, make a few substitutions and see if it holds true (and since we already know FF11<>FF12, voila). This is clearly mathematics at its finest.

I know this is a joke thread, but it bugs me when my students do this, so I feel compelled to correct you. D:

"Set them equal and see if it holds true" doesn't prove anything. In order for the process to work, you need to start with an equation that is known to be true; as long as you do the same thing to both sides of the equation, you know that whatever you get at the end is also true. For instance, the following "proof" does not demonstrate that -1 = 1:
```    -1 = 1
(-1)^2 = 1^2 (square both sides)
1 = 1   (oh look, it's true!)```

Starting with a false statement doesn't tell you anything (it doesn't even imply that your final result is false!).

Sadly I've seen graduate students in math make this same mistake....
Jul 02 2009 at 8:12 AM Rating: Excellent
125 posts
Let's say we want to show that X<>F.

We also know F=Y and X<>Y

So if we say X=F=Y, we know this to be untrue.

So then: X<>F
******************

-X=X

-X^2=X^2

SQRT(-X^2)=SQRT(X^2)

+-X=+-X

Edited, Jul 2nd 2009 12:18pm by Callipho
Jul 02 2009 at 8:30 AM Rating: Excellent
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Callipho wrote:
Let's say we want to show that X<>F.

We also know F=Y and X<>Y

So if we say X=F=Y, we know this to be untrue.

So then: X<>F

Well, I'm not trying to step on anyone's toes here...but I'm not sure what this has to do with your original proof. =x

Callipho wrote:
-X=X

-X^2=X^2

And being nitpicky, you didn't do the same thing to both sides there. =< You took the square of the right side, but took the negative of the square of the left. (If you're squaring -X you have to square the whole thing, not just the X part.)

I suspect I'm pushing into obnoxious territory now, so I'll shut up. =x
Jul 02 2009 at 8:37 AM Rating: Excellent
125 posts
It's cool, I really don't mind, even if I am wrong. I just want you to prove to me that you're right rather than just taking your word for it :-)

But anyways, the point of the first statement was that you can complete a proof by starting with a statement that you don't know to be true, with a simple substitution.

Second piece, there are special rules when it comes to sqrt and ^2. You still end up with the same answer of +-X=+-X. Your example doesn't prove anything but in that one example you don't complete your proof by starting with a known false statement.

I clearly wasn't even following these rules when I did my joke proof above, since I didn't use +- and randomly floored something but whatevs o.O

Edited, Jul 2nd 2009 12:43pm by Callipho

Edited, Jul 2nd 2009 12:50pm by Callipho
Jul 02 2009 at 8:58 AM Rating: Excellent
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Well in that case... >=D

Quote:
But anyways, the point of the first statement was that you can complete a proof by starting with a statement that you don't know to be true, with a simple subsitution.

Unfortunately that is not true. =( For an example of why it isn't, see my -1 = 1 "proof" above.

The fundamental logic at work here is that if we know X and Y are the same, then for any function f, f(X) and f(Y) must also be the same (that is, X=Y implies f(X)=f(Y)). However the converse is only true for one-to-one functions, those which never "repeat" any value in their range. Taking f(x) = x^2, for example, f(X)=f(Y) does not imply that X=Y; if X and Y are negatives, their squares are still the same.

Quote:
Second piece, there are special rules when it comes to sqrt and ^2. You still end up with the same answer of +-X=+-X. Your example doesn't prove anything but in that one example you don't complete your proof by starting with a known false statement.

The only reason there are "special rules" is that x^2 is not one-to-one, and hence it has no inverse function. We use square roots to "undo" squaring, but without additional information it is not possible to tell whether the positive or the negative result is correct. It gets worse with periodic functions -- if sin(x) = 0, there are infinitely many possible values of x, namely all the integer multiples of pi.

My example shows that there is at least one case in which starting with a false statement nevertheless results in something true. Ergo, one cannot assume in general that starting with a statement that may or may not be true will result in a statement reflective of the original's truth value. =3

Anyway, I'm not a big fan of trying to applying rigorous logic to things that are obviously jokes, and I did laugh out loud at your original post. :) I would've kept my mouth shut except that, being a professional mathematician, I was incited to blind rage by your later comment. :P
Jul 02 2009 at 9:49 AM Rating: Excellent
125 posts
Quote:
Unfortunately that is not true. =( For an example of why it isn't, see my -1 = 1 "proof" above.

The fundamental logic at work here is that if we know X and Y are the same, then for any function f, f(X) and f(Y) must also be the same (that is, X=Y implies f(X)=f(Y)). However the converse is only true for one-to-one functions, those which never "repeat" any value in their range. Taking f(x) = x^2, for example, f(X)=f(Y) does not imply that X=Y; if X and Y are negatives, their squares are still the same.

I saw your example and I was showing an example of how it can work. In my example you try to show X is not equal to F using the knowlege that X is not equal to Y and F equals Y making a substitution. Maybe you would prefer this to be called not a proof but rather a simple reasoning exercise but it achieves the same thing.

I am seeing this as more of as if-then statement.

If X=F then X=Y which we know to not be true.

Same here, if FFXI=FFXIV then FFXI=FFXII which we know not to be true. The actual math of getting there might be silly but that's the logic.

Sometimes, we lose sight of simple logic when looking at a bigger textbook picture. It is the ability to reason that makes us special.

Edited, Jul 2nd 2009 2:39pm by Callipho
Jul 02 2009 at 12:51 PM Rating: Good
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Callipho wrote:
I saw your example and I was showing an example of how it can work. In my example you try to show X is not equal to F using the knowlege that X is not equal to Y and F equals Y making a substitution. Maybe you would prefer this to be called not a proof but rather a simple reasoning exercise but it achieves the same thing.

Ohh, I see what you mean. Yes, if it is known that X <> Y and F = Y, it's of course obvious that X <> F. However, that is not the same thing as your FFXI / FFXIV proof -- in the latter you started with an equation and transformed both sides repeatedly. In that process you have only proved your result is true if the original equation is.

Semantically, in the FFXI[V] proof you started by assuming something that you know isn't true. In the F, X, Y proof you assumed something that is true; it just happened to be an inequality instead of equality. (If you had started off saying "given X <> Y and F = Y: assume X = Y..." you would be in a similar situation to the FFXI[V] proof.)

Edit:
Callipho wrote:
I am seeing this as more of as if-then statement.

If X=F then X=Y which we know to not be true.

Same here, if FFXI=FFXIV then FFXI=FFXII which we know not to be true. The actual math of getting there might be silly but that's the logic.

Perhaps I just didn't read you clearly, but the process you appear to be describing here is a proof by contrapositive. That is, if you want to prove that X implies Y, it suffices to show that (not Y) implies (not X). If that's what you meant, it was not obvious to me from your exposition. =<

Edited, Jul 2nd 2009 4:53pm by analysis
Jul 02 2009 at 7:00 PM Rating: Excellent
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Jul 02 2009 at 9:58 PM Rating: Good
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This topic makes me wanna kill myself with my stupidity.

Vissic wrote:

...I wish I was smarter...

I lol'd
Jul 02 2009 at 10:53 PM Rating: Default
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Quote:

FF11 = FF12.41

That's as far as we get without cheating.

And yes, FFXI was pretty much FFXII snd a half.

So.. does that mean FFXIV will be FFXV and a half?

Edited, Jul 3rd 2009 2:55am by Shazaamemt
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