uncool

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About uncool

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  1. Zero Element Equivalency

    Heh. I thought it was suspiciously similar, but forgot conway had been banned.
  2. Zero Element Equivalency

    You're providing more equations, but not answering the ones I have. If you dispute my equations, which of these is wrong? Does 1 = n/n? Does n/n = (-0)*n/n? Does (-0)*n/n = (-0)?
  3. Zero Element Equivalency

    We can then divide by n: 1 = n/n = (-0)*n/n = (-0) where the first and last equalities are from the fact that division is supposed to "undo" multiplication, and you've already agreed to the middle one. But I just noticed something I'd consider worse: you have the equation 1*(-0) = 1. The main reason 1 is important is that it is the multiplicative identity, that it multiplied by anything is that thing. Breaking this pretty much breaks multiplication, and makes inverses all but useless.
  4. Zero Element Equivalency

    The statement that inverses are unique is not a postulate, but a theorem. You have to break more than that statement to get things to work. For the proof that 1 = (-0): n = (-0) * n/(-0) = (-0) * n, right?
  5. Zero Element Equivalency

    The term "unique" in mathematics means only one. If you can't use the normal rules of equality, why use that version of equality at all? Do you agree that (-0) * n/(-0) = n?
  6. Zero Element Equivalency

    Actually, the fact that multiplicative inverses are unique is a basic fact. If n/(-0) = n, then under the usual rules of equality, we can multiply both sides by (-0): (-0) n/(-0) = n (-0). The usual definition of division then tell us that (-0) n/(-0) = n. We therefore have that n = n(-0). Finally, we can divide by n, and get 1 = (-0). So for what you are saying to make sense, you have to deny either: the ability to multiply both sides of an equation by the same number, the definition of division, the ability to divide both sides of an equation by a nonzero number, or transitivity of equality.
  7. Zero Element Equivalency

    If 0 + 0 is not equal to 0, then 0 doesn't have the property of being an additive identity (with respect to that equivalence relation). 1 already has a multiplicative inverse: 1. If n/(-0) = n, then it's not hard to deduce that (-0) = 1, unless you are assuming that = has very few properties in common with what we usually think of as equality. In short, your idea takes away many of the things that make fields useful in the first place.
  8. General topology

    I'm guessing they mean the product in the infinite product of the real line. Have you tried applying the definitions of the two topologies?
  9. Size & Gravity - Is General Relativity Incorrect?

    No. Newton's laws are still accurate for liquids and gases; the only difference is that they have to be analyzed through densities (note: not necessarily mass densities). The laws are still accurate. Because the sun is much, much, much, much closer than anything else in the galaxy. It's not because the Sun is more dense. It's that everything else is really, really, stupendously far away - so Newton's law of gravitation says that the corresponding force is tiny compared to that of the Sun.
  10. Size & Gravity - Is General Relativity Incorrect?

    The forces are, by Newton's third law, equal (and opposite). The accelerations are inversely proportional to the mass, by Newton's second law - so, as an interstellar cloud will generally be more massive than a planet, the planet's movement will be more affected. If you believe otherwise, then you are rejecting Newton's laws. Let's take interstellar gas out of the picture for a moment (as that runs into definition issues - interstellar literally means "between stars"). Instead, let' focus on galaxies. Yes, I have heard of stars orbiting galaxies (or, more precisely, orbiting as part of a galaxy). The closest thing to your statement is that, say, the acceleration of the Earth is more affected by the Sun than by the galaxy. Is that what you are trying to talk about?
  11. Size & Gravity - Is General Relativity Incorrect?

    What, precisely, do you mean by this? I think this is central to your claims.
  12. Size & Gravity - Is General Relativity Incorrect?

    Two things. 1) There is no part that says that; it isn't even true in general. More specifically: there are systems of objects where one object is not attracted towards the center of mass, but instead towards a nearby mass. This is clearest, for example, in the Sun-Earth-Moon system; the moon is attracted to the Earth, not to the center of mass of the Earth and Sun. 2) In the case of an object being attracted to a massive (that is, having mass) sphere, that in't separate from Newtonian gravity. It's a direct consequence (via the shell theorem, as Mordred says). As such, do you reject Newtonian gravity?
  13. Size & Gravity - Is General Relativity Incorrect?

    My apologies - I mistook your enthusiasm for that of the newly-"initiated". Good on you for keeping up that enthusiasm! I would say that even in the OP, the thread should clearly have been at the level of Newton's laws, and simple integration. I think that there already as a problem just with intrinsic vs extrinsic properties, as I plan to explain.
  14. Size & Gravity - Is General Relativity Incorrect?

    Unified Field: how much of standard physics do you accept? Do you accept Newton's laws? Newtonian gravity (as a nonrelativistic approximation)?
  15. Size & Gravity - Is General Relativity Incorrect?

    Mordred - I'm guessing that you just recently learned a lot of relativity, and really liked it. Which is good, but it's not the level appropriate for this conversation. This should be possible to discuss just using Newton's laws and Newtonian gravity - and probably very little in the way of integration.