April 17th, 2017, 03:24 PM  #21 
Senior Member Joined: Jun 2014 From: USA Posts: 364 Thanks: 26  
April 17th, 2017, 03:25 PM  #22 
Senior Member Joined: Aug 2012 Posts: 1,971 Thanks: 550  
April 17th, 2017, 03:25 PM  #23 
Senior Member Joined: Jun 2015 From: England Posts: 844 Thanks: 252 
So what is a random number?

April 17th, 2017, 03:26 PM  #24 
Senior Member Joined: Jun 2015 From: England Posts: 844 Thanks: 252  
April 17th, 2017, 03:31 PM  #25 
Senior Member Joined: Jun 2014 From: USA Posts: 364 Thanks: 26  You first need a sample space containing numbers (as opposed to shoes, etc. ...). Using some method of selection that assigns probabilities to the numbers in the sample space, you select a number. The selected number is then a randomly selected number. There are many methods of selection, the flipping of a fair coin example above being one of them if H=1 and T=0 where {0, 1} is the sample space. More relevant to the OP, if all numbers have an equal probability of being selected, you have a uniform distribution over the sample space. In the coin example, assuming a fair coin, we have a uniform distribution over $\Omega = \{0,1\}$. 
April 17th, 2017, 03:32 PM  #26  
Senior Member Joined: Aug 2012 Posts: 1,971 Thanks: 550  Quote:
Please refer back to the EXTREME amount of time and effort I put into your posts about shifting intervals a few weeks back. I struggled to understand your ideas at that time. I say to you as clearly as I can, and for the very last time: Your exposition in this thread is far more murky than those posts. There's simply nothing for me to work with. I can't repeat that any more and won't. I have spent more than enough time on this exposition which is simply not understandable to me in the least. Quote:
Quote:
We all have lives. Everyone posts for their own reasons. If you want me to spend any more time on your proof you're going to have to make another pass at clarity. As one specific example, you keep going, "And now we have two possibilities ... and now we have three possibilities ..." and at the very end you wave your hands and say, "And so we've selected a natural number uniformly." I see no such proof in what you've written. Now that's a specific criticism. Last edited by Maschke; April 17th, 2017 at 03:37 PM.  
April 17th, 2017, 03:35 PM  #27 
Senior Member Joined: Jun 2015 From: England Posts: 844 Thanks: 252 
Both posts 21 and 22 demonstrate (in their own way) my philosophical point that statistics, including probability, is an applied subject and that we are trawling pure maths (for good reasons) for models to be able to manipulate material in statistics. But that like all models these will be imperfect somewhere. I do not have time to demonstrate further tonight, but I will leave you with the question Have you investigated the application of the Dirac delta to this issue? It would seem to me to be a worthwhile line of enquiry. https://www.google.co.uk/?gws_rd=ssl...+in+statistics 
April 17th, 2017, 04:04 PM  #28  
Senior Member Joined: Aug 2012 Posts: 1,971 Thanks: 550  Quote:
You're really pushing to make a point that doesn't apply here. The theory of distributions in functional analysis is very well understood mathematically. It doesn't bear on the problem at hand and you have not demonstrated any connection.  
April 17th, 2017, 04:05 PM  #29  
Senior Member Joined: Jun 2014 From: USA Posts: 364 Thanks: 26  Quote:
That's not to dismiss what you're saying, just that I don't understand where you're going with this.  
April 17th, 2017, 04:12 PM  #30 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,341 Thanks: 2463 Math Focus: Mainly analysis and algebra  

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natural, random, real, selecting, uniformly 
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