# discountbrains

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1. ## Where to submit my proof that the set of real numbers can't be well ordered

I will now show that there are subsets of R such that there are no order relations which have a min for iit. Let T=(t,s). Now for the usual ´<'and a string of elements a,b,c,d,... all in T, we might have t<a<b<c<d<...<s. We might reorder these and still get t<*b<*d<*a<*c<*....<*s. Notice there is no way to produce a number z in T such that z≤*x for all x in T. Each letter has a position in the order or a slot and another letter is put in that position by the reordering, <*, so any new element in that slot has another element <* less than it just as with the original ordering <. Often I drift into little daydreaming sessions and think about how I might do something. Ive played with trying to reorder sets before. Now I might have found a use for this.
2. ## Where to submit my proof that the set of real numbers can't be well ordered

But how will you argue if you get asked why it also holds for <∗ This might be a good question. I think that the fact this needs to work for all subsets of R means this is true. Do we have to ban such sets? You are right; how exactly do I know what you asked? I think I can pick any subsets of R I want and pick any order. Will this fly?
3. ## Where to submit my proof that the set of real numbers can't be well ordered

How is this for an anology in my previous post: If I have a pet tiger and it bites me(=the existance of WO). If I feed it (= sets S or T are possible) it wont bite me. If it bites me anyway Iḿ in the hospital and cannot feed it. So now what? This is kind of a puzzler. I know my previous post about running into infinity is a bit vague.It was something going on in my head: I messed around with trying to wo stuff for years and it seems that u always end up dealing with something going to infinity. BTW, I thought there was nogreater number than c. Ive forgotten much of this stuff. No, I dont necessarily believe you can have wo without ac. You have told me you could. looked at your references and find them interesting. Iĺl try harder.
4. ## Where to submit my proof that the set of real numbers can't be well ordered

Sorry for wasting all this time insisting Im correct. You are ABSOLUTELY right. My assertion before had several fatal flaws. To save face I never put the word Proof at the top of my text. Like I said this was submitted for a critique. To begin with I asserted that <* is a supposed WO for ℝ. Intuitively we see a WO ,<', seperates the elements of each set so there already can't be some x,y,a∈S , with x<'a<'y. Now, let me try this: Suppose <* is any total order relation on ℝ. And <* is not the usual order <. There are nonempty subsets S of ℝ such that for any a,b∈S ∃x∈S, a<*x<*b (right?). So, if S has a min z then z≤*x for all x∈S. Let T=S\{z}, for any u∈T there exists another x∈T such that x<*u. Which implies there is no min in T for <*......Correction: I don't need this set S above. I had been trying to prove this by contradiction assuming <* is a WO. BUT, if <* is a WO I cannot make the "dense" set claim above. I think I just proved it directly-I hope. That is, ∃T⊂ℝ such that for any a,b∈T ∃x∈T , a<*x<*b. This is all of course based on the assumption there is no knowledge of well ordering relations or the AC. In this iteration am I already assuming no <* can be a WO at the start? I don't think so. To negate my claim one would also have to prove if <* is a WO you can't construct sets S and T above. Im going to try to think of a real world analogy to the idea of my proof.
5. ## Where to submit my proof that the set of real numbers can't be well ordered

Thank you for taking the time and effort to help me with this. I have alittle book called Ëquivalents of the Axiom of Choice which mentions weaker forms and numerous forms. Clearly many people have thought about this stuff a long time. The natural numbers is a subset of the reals. All I need to do is show there is at least one subset of the reals that doesnt have a <* l.e. to prove my point. Yeah, I am not approaching this with the precision I would have been doing if I were taking a class for a grade. I probably wouldn get by with some of this.....Back in the 1980s I showed what I thought was a WO of [0,1] to a math prof at the Univ of Denver. He walked over to his blackboard, picked up a piece of chalk, thought for a few seconds and wrote out two infinite strings of numbers and asked me which one was greater with my order. I said uh oh and left. I will look at your suggestions. A possible flaw in my hypothetical ordering is that I might be thinking of it in a usual sense. But, there just seems to be no other way. Any way you look at it you run into infinity somewhere. Again, I say all I need to do is show there is one subset that no l.e. can be found with the assumed WO to prove my assertion.
6. ## Where to submit my proof that the set of real numbers can't be well ordered

wtf made numerous reemarks that my thinking is seriously flawed. No problem there. Then wtf tells me I proved my assertion for dense sets and nothing else. If my proof is valid for these why does it not prove my assertiion? This makes no sense. The essence of the proof is if you can show there is no <* l.e. for some subset in the collection you cant say this works for ALL subsets in the collection which is what WO requires-if Im not mistaken. Then he talks about the set of natural numbers. Well, of course. This is obvious Its like the very definition of a WO set. Then he mentions ordinals. I don know what ordinals are. Actually, I know a little more about them than I let on. Something I dont understand is they seem to all be ordered the same way and must all be well ordered so whatś the distinction? And, whatś the use? Iĺl get pushback from wtf for this. wtf mentioned other models of set theory that allow well ordering without the need of the AC. I truly want to see these. I hope he will post something for me. I guess the natural numbers being well ordered is supposed to contradicts my proof.
7. ## Where to submit my proof that the set of real numbers can't be well ordered

Iḿ not proving anything by this. I just thought it was kind of a fun thing to do. Don know if its good for much. I thought one could define different kinds of addition. Using the usual addition you get interesting results. Or you might say 0.1265+ 0.0018=0.1373... or all kinds of ideas. Interesting. I didn know this. We proved that a line has the same number of points of this square in topology class a different way. I see it was Gödel who I should have said was associated with the CH Actually, I quickly realised my construction could prove this Cantor thing. i
8. ## Where to submit my proof that the set of real numbers can't be well ordered

OK then. I know of his very clever diagonal proof thing which was a bit different than this.
9. ## Where to submit my proof that the set of real numbers can't be well ordered

No.no, no. Yes you showed there are other sets of reals that can be WO even without AC just like the natural numbers can. But, I said above that the AC guarantees every set can be WO. Of course, we are in agreement in what you said. It looked like taeto said exactly what I had said above. Let me take this opportunity to show my little math construction-may be unrelated and of little value: Consider the interval I= [0,1] and draw the plane XxY. Let each point in the plane (x,y) be constructed from a number a in I such that x=the 1st digit and every other digit after that of a and y=the 2nd digit and every other digit after that of a. For example if a=0.297051... then x=0.275... and y=0.901...You could plot these numbers on XxY and draw any kind of line or any shape in this area and it would be a subset of I. Also, this is a way to make a bijection from I to this plane. I wonder if anyone has done this before.
10. ## Where to submit my proof that the set of real numbers can't be well ordered

OK, I see what I did. That a set can be WO depends on the AC. The two are equivelent statements. What I showed is WO does not exist naturally on its own. Its like saying if we can live on air we do not have to grow food and we know the first part is impossible. What I did was just an exercise. Of course something like this could never overturn 100 years of history. Of course it cannot be that simple. If a set is WO then there you have your set of numbers for the AC. Yes, its clear the natural numbers can be WO, but my thesis was that not every set can be WO. If you accept the AC then of course you say they can.
11. ## Where to submit my proof that the set of real numbers can't be well ordered

T in this case has the same order relation <* as S, We sometimes write (S,<*) and (T,<*). There is no l.e. in T with this order relation is there? We cannot make up a new order relation for each set we encounter. About AC imples WO: WO implies AC which implies Zornś Lemma implies Maximality Principal (the one with ever chain has a greatest element) and I don know what else. WO implies AC. They all imply each other or are equivalent. We proved all this stuff in a topology cjass I took or the professor did. Years later I wrote out proofs of my own to see it I could do it, Its prtty abstract stuff. Oh, and the Continuum Hypothesis is also in these equivallent statements.
12. ## Where to submit my proof that the set of real numbers can't be well ordered

WAIT A MINUTE! HOLD THE PHONE! I was right all along. I just need to put more detail in my proof. This proof is by contridiction. For suppose we say we have a WO, <*, for ℝ then for any S⊂ℝ there is an a∈S such that a≤*x for all x∈S. Now <* totally orders ℝ so for any a,b∈ℝ a<*b or b<*a. If T=S\{a} all x∈T,x≠a are the same as those in S and are ordered the same. We have T={x:a<*x and x∈S}. But, where is the l.e. of T in relation to <*? There is none. Therefore <* is not a WO of ℝ. About the subsets needing to be dense I threw that in at the beginning so there would be no argument about holes in the subsets. WO says ALL subsets have to have a l.e. Just pointing out one subset that doesn’t have a l.e. is sufficient. Yeah, I know I don like google either. First of all I don like the name. I was unhappy they bought youtube-about the best site on the web. Without the auto correct this leaves off the ´. Cannot even type an example.
13. ## Where to submit my proof that the set of real numbers can't be well ordered

I´m going to delete my post. What I was really trying to say is any well ordering is defined in a certain way (even though we may not know how its defined). Given any WO one can define a set (or rather a set exists) which has exactly the wrong properties for it to have a least element according to this well ordering. What I did does not show this. Iĺl have to say Iḿ a bit rusty at this and have not thought about this in depth in a lot of years.
14. ## Where to submit my proof that the set of real numbers can't be well ordered

I gave an answer using a library computer and didn keep track of the time limit. It was completely lost. Iĺl have to do it again. Iḿ thinking Iḿ sticking to my original statements. As I said before if a order relation, <*, WOs the set of reals there has to be a l.e. according to <* in every possible subset of the reals. If every possible subset cannot be constructed there is no guarantee a subset made up of elements each from each subset of the reals exists either. I like this Chromebook yes and no. There are a number of limitations, but its easy to carry anywhere. There is no delete' key.You have to use backspace. I think I finally found out how to disable this auto correct.
15. ## Where to submit my proof that the set of real numbers can't be well ordered

Yes, it's inconceivable how a dense set can be turned into a 'discrete' set of numbers-what I was trying to depict there. I haven't found a way to stop this absurd autocorrect on this Chromebook either.On thinking of this more I concluded we could consider any subset whatever no matter the structure with <*. Does that need to be proved or taken as an axiom?. Such a set I constructed doesn't have a l.e. But, guess what, saying any set can exists implies a set satisfying the AC exists. So, again this says the whole notion is undecideable.
16. ## Where to submit my proof that the set of real numbers can't be well ordered

Well thanks, wtf. The real idea behind my effort is that I've always noticed that when you try to come up with a well ordering for the reals there is always a set who's definition is the very thing that violates the ordering. My use of intervals is not a good example. Let me see if I can come up with a construction that works. Let me try this: Suppose A has a l.e. a with respect to <*. Now comsider B=A\{a}. Then a is not the l.e. of B. Your WO hyp says B has a l.e. b and a<b since b is inA. A and B are dense so there exists an x such that a<x<b . x can't be in B..... Anyway, this all leads to a contradiction. I would say the WO says all subsets of the reals defined in relation to <* have a l.e. in telation to <*. So, I think I can speak of them as interval in relation to <*. I hope I don't sound like I'm going around in circles. Yes, I need more thought on this; no doubt you'll tell me I need a lot more thought....OK, now I think I know what you are saying: If any set is WO it is turned into the form a1.a2, a3, ..., but I'm saying for any WO there will always exist a set that can't be turned into this structure. I realized I haven't really proven anything. While I believe any ordering can select a group of numbers it can't find a l.e. for I have to show just how this works.
17. ## Where to submit my proof that the set of real numbers can't be well ordered

I'm going to look more closely at your argument. I knew I should have defined more precisely what I mean by 'complete". I'm not saying 'completeness'.I got my definition from an introductory math analysis book where they say a set is 'complete' (need to check the exact definition) if all the numbers of the reals are dense in it. In other words, it has all the numbers from the reals, x, such that a<x<b or it has no gaps in it. I know I need to be more formal than this. Of cpurse these are intervals with respect to <* rather than <. This is all I need to show because this is supposed to be a collection of all subsets. I believe I found a much easier way to write math than any of this stuff. I go to 'type math symbols' and just insert their symbols in my text in their space below then copy and paste the whole thing.
18. ## Does physics say my notion is incorrect?

This may not prove much at all. NASA did some of this in a nearly complete vacuum and I believe it failed. but, did they do it in a partial vacuum? I think what this guy is doing is quite a bit different than what they've done before. You can see it's quite a bit heavier than the others. Some claim these work better in a vacuum; I'd have see a carefully controlled experiment. I still say u don't see any flight technology jump into the air like this. It also looked like it didn't want to be moved out of the location it was in.
19. ## Does physics say my notion is incorrect?

I was going to leave for good, but I looked on YouTube to see if there were any new good 'lifter' videos. You gotta see this! https://www.youtube.com/watch?v=006d36WWyaQ Note how it instantly jumps into the air many times as he turns it on. He even holds it down then releases it and it jumps back like a spring.He also demonstrates there is very little wind or air movement.Of course, there would have to be some caused by the movement.
20. ## Where to submit my proof that the set of real numbers can't be well ordered

I could have just said look for "What's wrong with my thinking?" by George Heyer on Quora.
21. ## Where to submit my proof that the set of real numbers can't be well ordered

Exactly, the Zorn's Lemma and all these other theorems are dependent on the Axiom of Choice which of course is an axiom. I at this time just can't figure out what's wrong with my proof. The A of C has always troubled me some and I've heard it's trouble some others. Should I go ahead and paste my proof now or teaze a little longer? Certainnly there must be something wrong and I'll look ridiculous.....Next time I'll post it; I need to look over it omce more. Its been on Quora for several months and got no comments.
22. ## Does physics say my notion is incorrect?

The National Enquirer is not a very reputable source. Had u known this story for a long time or did u feel u better check up on it? I didn't know this was in the N E. Again no one ever gave me reasons why I'm wrong, but u did answer my original question. I get into a flurry of posts sometimes when I'm annoyed and leave these boards alone for many months otherwise. I want to leave u with one more thing before it's BYE. You've probably seen those many 'lifters' on youtube. I made something a little similar once with HV. It didn't lose weight or anything. But, I did notice every time I flipped the switch it jumped just a little. If u watch the videos of the 'lifters' you'll notice they instantly jump into the air. This couldn't happen if they were levitating by moving air alone. I'm not a helicopter pilot, but I'd say it takes several seconds for the helicopter to begin rising when the pilot gives it full power.
23. ## Does physics say my notion is incorrect?

U're right. I got enough answers. I thought I might get something I didn't expect, but got nothing new. One last question for beecee before I go: Explain this, Nixon was a friend of Jackie Gleason and he knew Gleason was interested in UFOs. When Nixon was pres he sent a car around to Gleason's home and took him to a building on a military base in FL. Inside were 4 small alien dead bodies. Gleason's wife said he was speechless for a week after seeing this.
24. ## Where to submit my proof that the set of real numbers can't be well ordered

I thought the Journal of the American Mathematical Society might evaluate my proof so I sent it to them. Their secretary said it didn't meet the criteria for an article in their journal so they can't publish it which is quite understandable. It's only 4 lines. It's on Quora, but no one has commented on it. Maybe I should send it to a math professor or two. This is really bazaar; I can't find anything wrong with it. Much work has been done for nearly a century saying what I did is impossible and math is not open to consensus-its either right or wrong. I only considered the case of the possibility of there existing a function to well order the reals. No other way is useful to consider. I may paste it here, but I want answers from people who really know this stuff.
25. ## Does physics say my notion is incorrect?

beecee that's not true .......About "physicists know what causes gravity" no one told me what u know did they? In my past experiments I tried charging metal plates above and below an object + below and - above with high voltage DC The plates attached to the ground. This would make the pbject - below and + above which is opposite the natural charge. This should have made the object lighter. Nothing happened. Of course not, single platres can't hold much charge and if carbon was used for the object there would be Avagadro's # of atoms in 12grams of carbon with 6x6.02x1023 electrons in a gmole. Most of them need not be caused to move to see an effect but this would take unimaginable coulombs of charge. There MUST be another way: oscillating waves.
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