|
Register | Sign In |
|
QuickSearch
Thread ▼ Details |
Member (Idle past 2295 days) Posts: 2870 From: Limburg, The Netherlands Joined: |
|
Thread Info
|
|
|
Author | Topic: 0.99999~ = 1 ? | |||||||||||||||||||||||||||
onifre Member (Idle past 2951 days) Posts: 4854 From: Dark Side of the Moon Joined: |
But even then, I don't think that it's particularly a hazard for creative people. Not true, there are studies that have shown a correlation between creativity and Bipolar disorders.
Hypomania:
quote: Don't ask why I know this. Sorry for off-topic reply. - Oni
|
|||||||||||||||||||||||||||
Dr Adequate Member (Idle past 285 days) Posts: 16113 Joined: |
Not true, there are studies that have shown a correlation between creativity and Bipolar disorders. But what you have quoted is something beginning: "A number of people with creative talents have reportedly experienced hypomania". OK, what proportion of people "with creative talents" (how is this quantified?) have "reportedly experienced hypomania", and what proportion of people without creative talents have "reportedly experienced hypomania"?
|
|||||||||||||||||||||||||||
AnswersInGenitals Member (Idle past 151 days) Posts: 673 Joined: |
Let's use 0.9(n) to designate the number with n 9's after the decimal point (followed by zero's). Then, for any integer n, no matter how large, there is a number halfway between 0.9(n) and 1.0 that is different from 0.9(n) and 1.0. Thus, for all n, 0.9(n) and 1.0 are distinctly different numbers.
The error made in many of the above posts that try to prove that 0.99999.... is the same (is equal to) 1.0 is in confusing "converges to" and "is equal to". These are distinctly different attributes. In mathematical terms, the set of all 0.9(n) is an open set. Let's call this set SNo (for open set of strings of nines). !.0 lies on the boundary of this set but is not contained in it. Let SNc be the closure of SNo, i. e., the set SNo plus all its boundary points. This set does include 1.0 (and, of course, all the 0.9(n) for all n points), but it is distinct from (it is a different set than) SNo. Now for a mea culpa. As erudite and definitive as the above sounds, there is a very good chance that I don't know what the hell I'm talking about. I'm really just throwing it out here to see if someone who does know what the hell they are talking about will comment on it.
|
|||||||||||||||||||||||||||
PaulK Member Posts: 17822 Joined: Member Rating: 2.2 |
quote: I don't think so. 0.999... IS the limit of 0.9(n) as n tends to infinity, and that is what we want to prove equal to 1. It's the series which converges to 1, not the number.(That's not to say that there might not be similar confusion in some of the posts).
|
|||||||||||||||||||||||||||
Dr Adequate Member (Idle past 285 days) Posts: 16113 Joined: |
Now for a mea culpa. As erudite and definitive as the above sounds, there is a very good chance that I don't know what the hell I'm talking about. This. You might want to look up the term "open set".
|
|||||||||||||||||||||||||||
onifre Member (Idle past 2951 days) Posts: 4854 From: Dark Side of the Moon Joined: |
OK, what proportion of people "with creative talents" (how is this quantified?) have "reportedly experienced hypomania" Since this is off-topic I figured you'd check out the link, which answered this question.
quote: Obviously, due to privacy, hard numbers are not going to be available. We can only go with those who have publicly stated it. The main point was in the symptoms, which, by understanding the symptoms, it should be easy to see the correlation between bipolar/hypomanic disorder and artists/creativity.
quote: Evidence Linking Mania and Hypomania to Creativity: From link:
quote: And one more link, if you care to read it: Bipolar Disorder and the Creative Mind quote: Not to drag this further off-topic, but from the above, you don't think there is enough evidence to suggest a correlation? - Oni
|
|||||||||||||||||||||||||||
Jon Inactive Member |
Stile writes: Jon writes: 1 = 3/3 = 1/3 + 2/3 = 0.3333| + 0.6666| = 0.9999| ≠ 1 I don't understand this. You went logically along until the very end. I don't (logically) see any reason why you put a "≠" in instead of a "=" at the end. What would make you do so? Yes. I was 'quoting' (sans-any-reasonable-indication-that-it-was-a-quote ) the paradoxical hypothetical that Dr. A had come up with (Message 119). My point was as Dr. A's point; in a system where 0.9999| ≠ 1, there is a paradox. My extension of this was that Mother Nature doesn't have paradoxes in the first place that she must then fix with some 'distinctness' criteria that closes the paradox by equating the apparently unequal. But, I will not go further into this here, because I have started a (still un-promoted) topic (Message 1) which is meant to address the relationship of our Math system to Reality. The rest of your post seems to have been based on your understandable misreading of my horribly ambiguous statement, and so I think we can discount it. Thanks,Jon [O]ur tiny half-kilogram rock just compeltely fucked up our starship. - Rahvin
|
|||||||||||||||||||||||||||
Jon Inactive Member |
The fact that 0.999.. < 1.1 shows that it cannot grow to infinity. I think there is a fine difference between growing to infinity and infinitely growing. I would say that the latter is possible in respects 0.9, etc., while still maintaining it has a value less than 1.0. Afterall, the number we are working with is infinite, is it not? With no proof eliminating infiniteness (not quite the same as infinity, I don't think), starting with 0.0 and adding the 0.9 cuts the remaining distance between 0.0 & 1.0 to 1/10 its previous size, no? 1.0 - 0.0 = 1.01.0 - 0.9 = 0.1 (1/10)(1.0) = 0.1 0.1 is 1/10 of 1.0 Now, if we add another 9, so 0.99, the remaining 1/10 distance is cut itself to 1/10 of its former size. I won't do the proof for that, but it seems more intuitive to me that as we added 9s, the distance between 1.0 and 0.0 would simply become infinitely smaller, but never be a gap bridgeable through the adding of infinite 9s or without rounding. (I hear the word 'Zeno' being whispered in my ear, but I am not sure why.) It seems that left as it is, Math can end up describing a paradoxical nature... or, a reality that is not Reality. I see no reason why Math could not permit such infinite divisions in contradiction to Reality, which clearly does not. (Damn, there's that 'Zeno' whisper sound again.) Now, I realize that it doesn't work this way, and so long as the MATHSYSTEM maintains the DISTINCTness criterion it too will not permit such infiniteness. But that it needs a check-sub-system to eliminate contradictions with Reality should be a good sign that the MATHSYSTEM and its parts do not follow necessarily from Reality (REALWORLDSYSTEM), just that we have found a way to make the system both internally consistent and eliminate its contradictions to Reality. Anyway, more on this relationship when my dern thread gets (if ever) promoted. Jon Edited by Jon, : zeros and such [O]ur tiny half-kilogram rock just compeltely fucked up our starship. - Rahvin
|
|||||||||||||||||||||||||||
Apothecus Member (Idle past 2411 days) Posts: 275 From: CA USA Joined: |
It might be interesting to see how people think which explanations are the ones that best convince them -- Huntard and Straggler and any other lurkers who had trouble with this issue. Aside from a couple off-topic posts, I've lurked here for a while. With regard to this thread, it seems to me that in order to not be found at night in a deserted lot in Chippewa Falls, naked, shivering, malnourished and bleeding from multiple self-inflicted shiv gashes, you need to fall into one of the following categories: 1. Geniune, honest mathematician2. Not a mathematician, but still really smart with things like physics or drink mixology 3. Not a mathematician but with a rudimentary grasp of calculus or other maths (thus not too intellectually invested in your own opinion either way) 4. Don't care, but like to rattle the animals' cages all the same I think I fall somewhere in the #3 category. I can grasp the concept as put forth, and since I'm blatantly ignorant to most of the rationale for objecting to why 0.9999.... should not equal 1, I can happily whistle "Bolero" as I scroll through this thread. It seems like a very straightforward idea on the surface, and as a committed #3, the surface is all I really care to see. Thanks for this discussion. Have a good one.
|
|||||||||||||||||||||||||||
lyx2no Member (Idle past 4716 days) Posts: 1277 From: A vast, undifferentiated plane. Joined: |
Is Zeno by any chance whispering "For get about that turtle race thing: I was wrong."? Zeno couldn't solve it, but a lot of maths have been discovered since his day.
Now, if we add another 9, so 0.99, the remaining 1/10 distance is cut itself to 1/10 of its former size. I won't do the proof for that A proof for that? You are so out of your league. You are now a million miles away from where you were in space-time when you started reading this sentence.
|
|||||||||||||||||||||||||||
Dr Adequate Member (Idle past 285 days) Posts: 16113 Joined: |
I think there is a fine difference between growing to infinity and infinitely growing. I would say that the latter is possible in respects 0.9, etc., while still maintaining it has a value less than 1.0. Afterall, the number we are working with is infinite, is it not? NO. I see no reason why Math could not permit such infinite divisions in contradiction to Reality, which clearly does not. (Damn, there's that 'Zeno' whisper sound again.) Now, I realize that it doesn't work this way, and so long as the MATHSYSTEM maintains the DISTINCTness criterion it too will not permit such infiniteness. But that it needs a check-sub-system to eliminate contradictions with Reality should be a good sign that the MATHSYSTEM and its parts do not follow necessarily from Reality (REALWORLDSYSTEM), just that we have found a way to make the system both internally consistent and eliminate its contradictions to Reality. Anyway, more on this relationship when my dern thread gets (if ever) promoted. Pure gibberish.
|
|||||||||||||||||||||||||||
Jon Inactive Member |
Apothecus from Minnesotecus writes: ... Chippewa Falls... Hello my fellow Minnesotan Always good to be able to add some more cold, frigid sanity around here Jon [O]ur tiny half-kilogram rock just compeltely fucked up our starship. - Rahvin
|
|||||||||||||||||||||||||||
Jon Inactive Member |
Afterall, the number we are working with is infinite, is it not? NO. It's not? How many decimal places does 0.9999| go out to? Jon [O]ur tiny half-kilogram rock just compeltely fucked up our starship. - Rahvin
|
|||||||||||||||||||||||||||
Dr Adequate Member (Idle past 285 days) Posts: 16113 Joined: |
It's not? Of course not.
How many decimal places does 0.9999| go out to? Infinitely many, of course.
|
|||||||||||||||||||||||||||
Jon Inactive Member |
Dr. A writes: It's not? Of course not.
How many decimal places does 0.9999| go out to? Infinitely many, of course.
Care to explain? [O]ur tiny half-kilogram rock just compeltely fucked up our starship. - Rahvin
|
|
|
Do Nothing Button
Copyright 2001-2023 by EvC Forum, All Rights Reserved
Version 4.2
Innovative software from Qwixotic © 2024