My Math Forum Selecting a Natural and a Real Uniformly at Random

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April 17th, 2017, 04:24 PM   #21
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Quote:
 Originally Posted by studiot I actually said almost the exact opposite. Tell me what you think a random number is? For instance are 1 or 0 random numbers?
No, not unless you pick one by, for example, flipping a fair coin and assigning 1 to heads and 0 to tails.

April 17th, 2017, 04:25 PM   #22
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Quote:
 Originally Posted by studiot For instance are 1 or 0 random numbers?
They may or may not have been randomly selected. They are of course not random, each being a computable real number.

 April 17th, 2017, 04:25 PM #23 Senior Member   Joined: Jun 2015 From: England Posts: 891 Thanks: 269 So what is a random number?
April 17th, 2017, 04:26 PM   #24
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Quote:
 Originally Posted by AplanisTophet No, not unless you pick one by, for example, flipping a fair coin and assigning 1 to heads and 0 to tails.

So what is a random number?

April 17th, 2017, 04:31 PM   #25
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Quote:
 Originally Posted by studiot So what is a random number?
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, 04:32 PM   #26
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 Originally Posted by AplanisTophet So, if the problem is that you don't understand my OP because you feel it is "convoluted" and "incomprehensible," then please quote the first part of the OP that you feel fits that description and I'll address it. Fair enough?
No. It's time for you to write a clear version of your proof. I won't spend any more time on your current one.

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:
 Originally Posted by AplanisTophet 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 understand that your emotional attachment to your idea is keeping you from hearing me when I tell you that your exposition is too unclear for me to follow. You are the one who said I treated you with "disdain" and frankly that remark strongly disincentivized me to spend any more time on this. The burden is on you to start showing some good faith.

Quote:
 Originally Posted by AplanisTophet 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.
CPA ... CPA ... this is hitting some forgotten brain cells. Have you and I had a lengthy conversation somewhere else under perhaps different handles? I had a long convo with someone expressing alternative ideas a long time ago who said they did taxes and I can't for the life of me remember who or what or where.

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 04:37 PM.

 April 17th, 2017, 04:35 PM #27 Senior Member   Joined: Jun 2015 From: England Posts: 891 Thanks: 269 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, 05:04 PM   #28
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Quote:
 Originally Posted by studiot 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
To what issue? The Vitali set?

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, 05:05 PM   #29
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Quote:
 Originally Posted by studiot 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
In the context of assigning any positive value to the probability of selecting a natural number contained in a(n impossible, supposedly) uniform distribution over $\mathbb{N}$, the Dirac Delta seems intriguing in that an integral over a single point, 0, can yield a positive number, 1. Obviously it's not a real function in the standard setting. Nevertheless, consideration of this is imho a very tall order given what is stated in the OP. I feel I may be better off considering the Riemann Zeta analytic continuation in trying to assert that an infinite sum can equal a real number like -1/12 seeing as how the uniform probability over $\mathbb{N}$ is generally considered impossible because it sums to infinity.

That's not to dismiss what you're saying, just that I don't understand where you're going with this.

April 17th, 2017, 05:12 PM   #30
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Quote:
 Originally Posted by Maschke This is a very disingenuous argument that utterly fails to understand the nature of mathematics. I'm not sure how it creeped in here.
Perhaps you just aren't intelligent enough to understand it.

 Tags natural, random, real, selecting, uniformly

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