How does Gandalf know that the ring's destruction will imply Sauron's "death"? During the last debate, Gandalf says:     "Concerning this thing, my lords, you now all know enough for the    understanding of our plight, and of Sauron's. If he regains it, your valour    is vain, and his victory will be swift and complete: so complete that none    can foresee the end of it while this world lasts. If it is destroyed, then    he will fall; and his fall will be so low that none can foresee his arising    ever again. For he will lose the best part of the strength that was native    to him in his beginning, and all that was made or begun with that power will    crumble, and he will be maimed for ever, becoming a mere spirit of malice    that gnaws itself in the shadows, but cannot again grow or take shape. And    so a great evil of this world will be removed."   How does Gandalf -or any other of the wise- know that Sauron will indeed be crippled to such an extent if the ring is destroyed (and why is this not already mentioned during the council of Elrond)?    To understand where this question comes from, it may be useful to know that Peter Jackson's depiction of Sauron's incapacitation at the end of the Second Age is controversial. It is not said in the books that a fit Sauron has his ring-finger cut of and then suddenly disintegrates. The text rather suggests that Gil-Galad and Elendil maim Sauron, whereafter Isildur cuts the ring off a near-incapacitated Sauron.    It was brought to my attention that this question may superficially be viewed as a duplicate of . However, that question does not ask after the method by which the wise determine that Sauron will be crippled by the ring's destruction. That is, it asks whether, not how. I find this important because during the last debate Gandalf urges the leadership of Gondor and Rohan basically to bet everything on this single assumption. So one would think/expect that Gandalf has solid proof for his assertion.
Did the Council of Elrond know that destroying the Ring would destroy Sauron? Did they decide to destroy it simply because they were Wise and knew it was dangerous to wield? Did they create the Fellowship simply because they were heroic; and decided to face Sauron after the Ring was destroyed?  Or did they know that destroying the ring would defeat Sauron, and they wouldn't actually have to do anything once that is taken care of?
Making an MFC application international I've got several large MFC applications here, and converting them into any other format is out of the question.  We're expanding into other markets, and would like to make the apps work in other languages and cultures.  So far, I've found occasional references as to what to do with Visual C++ version 6, with one mention that later versions of MFC have additional relevant features.  Searching MSDN gives me instructions on how to convert the apps to Unicode, which we already did.  I found nothing on MSDN on how to make languages multilingual once they're in Unicode, only a few older things using Google, and one book about internationalization using VC++6.  (We're using Visual Studio 2008 now, on XP and Vista.)    I make no claims for the strength of my Google-fu, and would be happy to be directed to things I've missed.  Is it reasonable to use the methods of VC++6, or should I use later features?  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In the construction of types of numbers, we have the following sequence:  $$\mathbb{R} \subset \mathbb{C} \subset \mathbb{H} \subset \mathbb{O} \subset \mathbb{S}$$  or:  $$2^0 \mathrm{-ions} \subset 2^1 \mathrm{-ions} \subset 2^2 \mathrm{-ions} \subset 2^3 \mathrm{-ions} \subset 2^4 \mathrm{-ions} $$  or:  "Reals" $\subset$ "Complex" $\subset$ "Quaternions" $\subset$ "Octonions" $\subset$ "Sedenions"  With the following "properties":   From $\mathbb{R}$ to $\mathbb{C}$ you gain "algebraic-closure"-ness (but you throw away ordering). From $\mathbb{C}$ to $\mathbb{H}$ we throw away commutativity. From $\mathbb{H}$ to $\mathbb{O}$ we throw away associativity. From $\mathbb{O}$ to $\mathbb{S}$ we throw away multiplicative normedness.   The question is, what lies on the right side of $\mathbb{S}$, and what do you lose when you go from $\mathbb{S}$ to one of these objects ? When is the sum of divisors a perfect square? How to automatically archive a directory? 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