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About uncool

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  1. Why? At most, all you've done is restate the basic premise: more particles exist than antiparticles. Just saying "More particles became real" doesn't explain the broken symmetry.
  2. Newtonian physics and classical (non-quantum) physics are the standard examples. Of course, when saying that, The Relativity of Wrong is required reading.
  3. As a note, the term "lower bound" refers to a specific order; something that is a lower bound with respect to one order may not be for another order. I have been assuming that in each case, "lower bound" referred to the <* order.
  4. I truly don't. I don't even see a reason why 0 should be a lower bound, let alone the greatest lower bound. It's an order, yes. That doesn't mean you can directly copy statements that are true for other orders. Arbitrary orders are defined as relations: given two numbers x and y, either x < y, or it isn't, with the requirements that either x = y, x < y, or y < x, and that if x < y and y < z, then x < z. That's it. wtf's list clearly defines an order on the reciprocals of positive integers, which is even a well-ordering.
  5. That's not how arbitrary orders are defined. Why must there be such a q? Your earlier attempt ("S = {m,n,o,...}") was better; at least it dealt with the actual definition and question at hand, and the argument could at least be repurposed to something somewhat meaningful. This "argument" is an attempt to ignore definition.
  6. I'm sorry, I couldn't make heads nor tails of what you were trying to say there. What is your proof that for any order relation <*, the set S = {0 <* x <* 1} has no minimum? I am not asking you to show that S is a set. It is a set. I stipulate that. But your proof depends on your claim that S has no minimum with respect to <*, and you have yet to prove that claim.
  7. Why should this exhaust S? You keep trying to wave away key parts of your proof. Something you should learn when attempting a proof: the things you most want to handwave are often the most important parts of the proof. Your attempted proof seems to come down to the claim that any infinite well-ordering is isomorphic to the usual ordering on the positive integers. That is, if a well-ordering is infinite, then it looks like m<n<o<..., and every element must be represented in that sequence. Correct?
  8. I truly don't know what distinction you are making here; the axioms are what give you the "material" or "structure" to "construct" things, and (usually more importantly) then provide a method to prove theorems about those things Constructing an uncountable set is easy. Use the axiom of infinity to get an inductive set; use the axiom schema of specification to get a set we think of as the positive numbers, and use the powerset axiom to get the powerset of the natural numbers. This powerset is uncountable, by Cantor's theorem.
  9. By constructing it, using the axioms of set theory.
  10. I said that for a specific reason: you keep trying to use a structure ("+*") that you fail to define, and then worse, you assume properties about it without proving those properties. That's not how a proof can work. You can define such a set. Basic set theory, axiom schema of specification. Prove it. Your attempted proofs have not been sufficient.
  11. Do you know why that formula works, in a geometric sense? (I don't plan to simply give an answer at the moment; simply giving an answer is uninformative, and someone recently asked the same question in the Homework Help section)
  12. There are countably many triplets of integers (a, b, c) such that a^2 + b^2 = 2c^2. There's even a method to find them. Do you know how to find a triplet (a, b, c) such that a^2 + b^2 = c^2?
  13. I realize why you want to be able to use it, but you have to demonstrate that it makes sense in the first place. To be honest, I think you are attempting to write a proof where you don't have an understanding of the underlying question, or of how a proof works.