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Obviously
 Post subject: Defining infinite sets  |  Posted: Mon Jan 20, 2014 4:00 pm

Original Member

Joined: Mon Aug 08, 2011 3:31 am
Posts: 45
Location: Norway

 I'm having some troubles doing this. The exercise is as follows:Given two infinite sets:S = { 5,10,15,20,25,... } andT = { 3,4,7,8,11,12,15,16,19,20,... }.Specify each of these sets by defining the properties Ps and Pt such that S = { x ∈ N : Ps(x) } and T = { x ∈ N : Pt(x) }.N is natural numbers btw.I tried defining the property of S like this:Ps = { x ∈ S : x ∪ |{0,1,2,3,4}| }This looks retarded, to put it bluntly, but I'm not sure what else I can do. I suppose I should instead try and define something like "every fifth element in N". Not sure how to go about this though. The book doesn't help. _________________"Reality is that which, when you stop believing in it, doesn't go away" - Philip K. DickDoes that apply to insane people too?
marnixR
 Post subject: Re: Defining infinite sets  |  Posted: Mon Jan 20, 2014 5:29 pm

Joined: Thu Aug 04, 2011 8:35 pm
Posts: 4798
Location: Cardiff, Wales

 sorry i can't help - this is so totally over my head _________________"Reality is that which, when you stop believing in it, doesn't go away." (Philip K. Dick)"Someone is WRONG on the internet" (xkcd)
Obviously
 Post subject: Re: Defining infinite sets  |  Posted: Tue Jan 21, 2014 1:55 pm

Original Member

Joined: Mon Aug 08, 2011 3:31 am
Posts: 45
Location: Norway

 I suddenly got the idea that I could use the difference in sets and came up with this:Ps = { x ∈ S : x ∉ {1,2,3,4,6,7,8,9} }I quickly realized this wouldn't do either.I really hope I survive this semester... _________________"Reality is that which, when you stop believing in it, doesn't go away" - Philip K. DickDoes that apply to insane people too?
Prometheus
 Post subject: Re: Defining infinite sets  |  Posted: Tue Jan 21, 2014 5:04 pm

Original Member

Joined: Sun Aug 07, 2011 8:58 am
Posts: 309

 Could you define S as something like the multiples of 5 of all the positive natural numbers? So N=1 would map to x=5, N=2 would map to x=10 and so on. Not sure how that would look notationally though, something like:S = { x ∈ N : 5N for all positive N }I know how you feel by-the-way. Who would have thought this maths stuff was so hard, hey?
Obviously
 Post subject: Re: Defining infinite sets  |  Posted: Wed Jan 22, 2014 9:14 am

Original Member

Joined: Mon Aug 08, 2011 3:31 am
Posts: 45
Location: Norway

 Prometheus wrote:I know how you feel by-the-way. Who would have thought this maths stuff was so hard, hey?I know this is supposed to be easy, but for some reason my mind gets stuck on trivial things. I thought of doing this through a bijection or something like you seem to suggest yet for whatever reason I thought that was not how I was supposed to solve it.Prometheus wrote:S = { x ∈ N : 5N for all positive N }I suppose something more is needed. Like having a function f : S --> N. Then something like f(s) --> n or whatever. Then having defining the function as being a property of S. I'll have to play around with it a little later I suppose.Thanks for the input! _________________"Reality is that which, when you stop believing in it, doesn't go away" - Philip K. DickDoes that apply to insane people too?
Obviously
 Post subject: Re: Defining infinite sets  |  Posted: Thu Jan 23, 2014 7:51 pm

Original Member

Joined: Mon Aug 08, 2011 3:31 am
Posts: 45
Location: Norway

 Obviously wrote:Prometheus wrote:I know how you feel by-the-way. Who would have thought this maths stuff was so hard, hey?I know this is supposed to be easy, but for some reason my mind gets stuck on trivial things. I thought of doing this through a bijection or something like you seem to suggest yet for whatever reason I thought that was not how I was supposed to solve it.Prometheus wrote:S = { x ∈ N : 5N for all positive N }I suppose something more is needed. Like having a function f : S --> N. Then something like f(s) --> n or whatever. Then having defining the function as being a property of S. I'll have to play around with it a little later I suppose.Thanks for the input!EDIT:Turns out I was overcomplicating things (as is typical for me). It should suffice with something like Ps = { x ∈ S : 5x ∈ N } I think. Oh well. _________________"Reality is that which, when you stop believing in it, doesn't go away" - Philip K. DickDoes that apply to insane people too?
iNow
 Post subject: Re: Defining infinite sets  |  Posted: Thu Jan 23, 2014 11:51 pm

Original Member

Joined: Thu Aug 04, 2011 11:40 pm
Posts: 5603
Location: Iowa

 Obviously wrote:Turns out I was overcomplicating things...Story of my life. _________________iNow"[Time] is one of those concepts that is profoundly resistant to a simple definition." ~C. Sagan
shlunka
 Post subject: Re: Defining infinite sets  |  Posted: Wed Sep 28, 2016 4:20 pm

Joined: Wed Aug 14, 2013 4:55 pm
Posts: 54
Location: Virginia, US

 I tried Kolmogorov complexity but it didn't work. _________________John Hancock was here.
Olinguito
 Post subject: Re: Defining infinite sets  |  Posted: Sun Jan 01, 2017 6:42 pm

Joined: Mon Aug 19, 2013 3:56 pm
Posts: 143

 My preferred definition of an infinite set:A set X is infinite iff it has a proper subset Y such that a bijection f:X→Y exists.However, the equivalence of this to other definitions of infinite sets may depend on the axiom of choice in Zermelo–Fraenkel set theory, on which modern mathematics is based. _________________Blog
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