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 12-02-2017, 08:18 PM #1 robert_utk old hand     Join Date: Jan 2005 Location: ValueTown Posts: 1,506 Are these two expressions “equal”? Short and sweet. Is this an allowed description of a uniform real distribution of numbers? From a formal mathematics perspective, can I say that: The random real numbers (0,1) Equals.... The random real numbers [1-.999999etc,.9999etc] Does forcing one of the inclusive boundaries to be an expression of the other inclusive boundary break a formal rule? Thanks!
 12-02-2017, 08:30 PM #2 RustyBrooks Carpal \'Tunnel     Join Date: Feb 2006 Location: Austin, TX Posts: 23,419 Re: Are these two expressions “equal”? Well, the problem is, I think, that .9 repeating equals 1. It's not "close to 1", it is 1. So you turned (0, 1) into [0, 1] and those are not the same. ETA: really I keep going back and forth. I could see an argument either way.
 12-02-2017, 08:42 PM #3 robert_utk old hand     Join Date: Jan 2005 Location: ValueTown Posts: 1,506 Re: Are these two expressions “equal”? Would both be an acceptable way to say “any number between 0 and 1” ? Granted, the simpler expression should be used for simplicity sake, but can you define one side as an expression of the other, such as (1-1,1)?
 12-02-2017, 08:50 PM #4 RustyBrooks Carpal \'Tunnel     Join Date: Feb 2006 Location: Austin, TX Posts: 23,419 Re: Are these two expressions “equal”? Sure? Theoretical math is not real big on doing arithmetic so it's common to see ranges like (1/2, sqrt(2)) and no one is going to make you say (0.5, 1.414...) But you should prefer to just say (0, 1) imo because this is literally what it's meant for
 12-02-2017, 08:56 PM #5 robert_utk old hand     Join Date: Jan 2005 Location: ValueTown Posts: 1,506 Re: Are these two expressions “equal”? Is (1-x,x) a valid expression of real numbers, so long as x is real? Thank you RustyBrooks
12-02-2017, 09:03 PM   #6
RustyBrooks
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Join Date: Feb 2006
Location: Austin, TX
Posts: 23,419
Re: Are these two expressions “equal”?

Quote:
 Originally Posted by robert_utk Is (1-x,x) a valid expression of real numbers, so long as x is real?
I dunno, seems fine to me. The rules are pretty fluid as long as it's clear what you mean.

 12-02-2017, 09:06 PM #7 robert_utk old hand     Join Date: Jan 2005 Location: ValueTown Posts: 1,506 Re: Are these two expressions “equal”? Yay!
 12-02-2017, 10:27 PM #8 heehaww Pooh-Bah     Join Date: Aug 2011 Location: Tacooos!!!! Posts: 4,268 Re: Are these two expressions “equal”? Pretty sure that in order to say (1-x, x) you have to specify that x >= 1/2 (if x=1/2 then that's the null set so that works).
12-03-2017, 12:52 PM   #9
RR
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Join Date: Sep 2002
Location: NOLA
Posts: 12,192
Re: Are these two expressions “equal”?

Quote:
 Originally Posted by RustyBrooks Well, the problem is, I think, that .9 repeating equals 1. It's not "close to 1", it is 1. So you turned (0, 1) into [0, 1] and those are not the same. ETA: really I keep going back and forth. I could see an argument either way.
There is not a (correct) argument either way. 0.9999 repeating is a real number and 1 is a real number. If 0.99999 repeating is less than 1 there exists a rational number x such that 0.99999 repeating < x < 1. No such rational number exists, so 0.9999 repeating equals 1, by the density of rational numbers.

If you were not saying you go back and forth on if they are equal, I apologize for misreading what you meant.

 12-03-2017, 10:54 PM #10 RustyBrooks Carpal \'Tunnel     Join Date: Feb 2006 Location: Austin, TX Posts: 23,419 Re: Are these two expressions “equal”? No, they are definitely equal. But consider, what's the largest number in the range (0, 1)? If you were going to rewrite the expression (0, 1) as [0, x], what's x? I can't think of a better candidate than .9 repeating.
 12-03-2017, 11:26 PM #11 heehaww Pooh-Bah     Join Date: Aug 2011 Location: Tacooos!!!! Posts: 4,268 Re: Are these two expressions “equal”? There is no largest number in the range, so you can't rewrite it in square brackets except as the expression [0,1] \ [0,0]U[1,1]
12-04-2017, 03:08 AM   #12
nickthegeek
journeyman

Join Date: Sep 2011
Posts: 216
Re: Are these two expressions “equal”?

Quote:
 Originally Posted by RustyBrooks No, they are definitely equal. But consider, what's the largest number in the range (0, 1)? If you were going to rewrite the expression (0, 1) as [0, x], what's x? I can't think of a better candidate than .9 repeating.
There is no "largest number" in that set. A set doesn't have to have a maximum. For instance, what's the largest number in R?

The (0,1) range does have an infimum and a supremum.

You can't find an x such as (0,1) and (0,x] are the same set. If you could, there wouldn't any need of discriminate between "(" and "[" in the interval notation.

12-04-2017, 10:35 AM   #13
robert_utk
old hand

Join Date: Jan 2005
Location: ValueTown
Posts: 1,506
Re: Are these two expressions “equal”?

Quote:
 Originally Posted by nickthegeek There is no "largest number" in that set. A set doesn't have to have a maximum. For instance, what's the largest number in R? The (0,1) range does have an infimum and a supremum. You can't find an x such as (0,1) and (0,x] are the same set. If you could, there wouldn't any need of discriminate between "(" and "[" in the interval notation.

I knew you guys and gals would know the answer, and help me learn as well! I know I should crack a book and learn such things on my own. However, my time is limited and devoted to a different problem.

What I *should* have asked was:

Can I say that....

(0,1) is interchangeable with (1-1,1)

Which I think is yes, from the help here from RustyBrooks

12-04-2017, 04:14 PM   #14
nickthegeek
journeyman

Join Date: Sep 2011
Posts: 216
Re: Are these two expressions “equal”?

Quote:
 Originally Posted by robert_utk Can I say that.... (0,1) is interchangeable with (1-1,1)
I can hardly see the point of this, but you can of course, since 1-1=0. (0,1) is even interchangeable with (44-44,73-72), but I can't see how this "result" can be of any use.

 12-06-2017, 02:54 PM #15 robert_utk old hand     Join Date: Jan 2005 Location: ValueTown Posts: 1,506 Re: Are these two expressions “equal”? When you want to relate the results of a problem involving (0,1) to the theoretical results of the same problem in (0,x) where x>1 then a particular nomenclature will arise. Thus the bounds become an expression of each other that are no as simple as just saying (0,x+1) if the new bounds are in fact (x-1,2x) or somesuch

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