April 17th, 2017, 01:48 PM  #11  
Senior Member Joined: Jun 2014 From: USA Posts: 210 Thanks: 6  Quote:
I am hoping someone can read the above and say what is wrong specifically. I was expecting Maschke to say something like "the mappings in part 3 of the process aren't uniform because 5 has a better chance of being selected than 7." I think they are uniform, but just trying to come up with something. Can anyone do this as opposed to spouting of the typical "there is no uniform probability on the naturals" argument. I am well aware of that argument, the proof for it, and why people say that. What in my proof specifically goes wrong, if anything? Two days almost and nothing here or at the physics forums where, in my experience, people will ream you quite quickly for posting pure rubbish.  
April 17th, 2017, 02:05 PM  #12 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,557 Thanks: 2148 Math Focus: Mainly analysis and algebra 
As I said, selecting an infinite binary sequence with equal probability is circular reasoning. You can only do it in theory. Any attempt in practice is nonterminating. Just like throwing a dart and measuring where it lands. In each case you assume that you have selected uniformly one of an uncountable number of items, so obviously it is possible to do so.

April 17th, 2017, 02:15 PM  #13  
Senior Member Joined: Aug 2012 Posts: 1,165 Thanks: 257  Quote:
In my opinion, complaining that you can't physically instantiate some mathematical idea is like saying that we can't be sure $\frac{1}{2} + \frac{1}{2} = 1$ because we can't exactly divide a physical substance in half and perfectly measure the result. After all, all physical measurement is approximate. This is a very disingenuous argument that utterly fails to understand the nature of mathematics. I'm not sure how it creeped in here. Last edited by Maschke; April 17th, 2017 at 02:24 PM.  
April 17th, 2017, 02:29 PM  #14  
Senior Member Joined: Aug 2012 Posts: 1,165 Thanks: 257  Quote:
It's a matter of genuine disappointment to me that you've decided that I'm being personally mean to you rather than making a mathematical judgment that your argument is convoluted and incoherent. A few weeks ago I spent many many hours patiently working through your flawed mathematical argument to help you clarify your understanding. I'm sad that in this case you don't realize that I'm doing exactly the same. At this point I've been through your argument about six or eight times and can't make heads or tails out of it. When I take the time to tell you that your argument is convoluted, incomprehensible, and doesn't even begin to show what you claim it does, I am doing you the service of allocating my time to helping you. I am very personally disappointed that you would rather conclude that I'm treating you with "disdain," your word. You have clearly let your emotions get the better of you here and you can't even see who your friends are. For that reason I need to step back and let you sort this out on your own. I would suggest that you make an attempt to write a much clearer version of your argument. That's a supportive suggestion, not an insult. I'm sad that you can't see it that way. Last edited by Maschke; April 17th, 2017 at 02:38 PM.  
April 17th, 2017, 02:33 PM  #15  
Senior Member Joined: Jun 2014 From: USA Posts: 210 Thanks: 6  Quote:
Probabilities and Infinite Sets In my OP I say "given" this binary sequence, then... So, you are not willing to give me that binary sequence because even though it's possible in theory, it's not in practice. Are you not willing to entertain the possibility of doing it in theory even if not practical as CRGreathouse was? Why not?  
April 17th, 2017, 02:52 PM  #16  
Senior Member Joined: Jun 2015 From: England Posts: 558 Thanks: 145  Quote:
How can you say my view is not relevant when you don't know what it is or take any steps to find out? And then you complain that noone is speaking to you anywhere. Do you wonder at that?  
April 17th, 2017, 02:53 PM  #17 
Senior Member Joined: Aug 2012 Posts: 1,165 Thanks: 257  Can you prove that? On a serious note, OP is quite correct to be dismayed by your claim that "... selecting an infinite binary sequence with equal probability is circular reasoning." That's entirely incorrect. It's certainly possible to select a random real in the unit interval. I understand that you meant to say that you can't do such a thing in the real world, but neither can you divide $1$ into two copies of $\frac{1}{2}$. Physical considerations are not relevant here. As OP is struggling with a construction based on the Vitali set, I truly fail to understand how physical considerations would enter into this conversation and I understand OP's dismay. Last edited by Maschke; April 17th, 2017 at 02:58 PM. 
April 17th, 2017, 02:55 PM  #18 
Senior Member Joined: Jun 2014 From: USA Posts: 210 Thanks: 6  I thought your view was relevant. I don't understand. It was helpful. I'm sorry if that's what you took from that. I thought you were pointing out that physicists, being concerned with the journey, wouldn't read past the "select a real in [0,1] at random part." Mathematicians, being concerned with the theoretical, would accept it.

April 17th, 2017, 03:17 PM  #19  
Senior Member Joined: Jun 2015 From: England Posts: 558 Thanks: 145  Quote:
Tell me what you think a random number is? For instance are 1 or 0 random numbers?  
April 17th, 2017, 03:23 PM  #20  
Senior Member Joined: Jun 2014 From: USA Posts: 210 Thanks: 6  Quote:
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On a side note, I was genuinely confused. You have been very kind in the past with your time. It's not something I expect of you and it is appreciated. Do you understand that I thought this time you were simply electing to blow me off? I stayed up late so as to hide easter eggs for my kid and made the OP, but I was exhausted working tax season. I wouldn't have posted this in the first place if it wasn't for the conversation in the other thread.  

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natural, random, real, selecting, uniformly 
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