Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20131016 04:10:22
Set notation for corresponding setsHi! and we wish to make the statement that 0 corresponds with a, 1 corresponds with b, etc., how would we go about doing that? Also, they are not the same set. A real world example might be moments in time and events in time where each event occurs in each moment. What would be the formal mathematical expression? Thanks! #2 20131016 04:23:38
Re: Set notation for corresponding setsI'd do it like this: The backwards E stands for "there exists". A bijection is a relationship that is 1 to 1 between the sets. http://www.mathsisfun.com/sets/injectiv … ctive.html http://en.wikipedia.org/wiki/Bijection Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #4 20131018 23:48:58
Re: Set notation for corresponding setsIn the same fashion, if we have a number line made up of all the real numbers and if there is a boundary within how do we say that we want to have the set of everything from a to b in terms of all reals minus everything except for what is in the set from a to b? I understand the set from a to b is a subset of all reals but how can it be defined as the set of all reals minus everything except what exists within the set a>b? On a related note, does anyone know of a good web site or book that teaches all about set notations? I checked out Khan Academy but there were only a few videos on the basics. Thanks. #5 20131019 00:42:14
Re: Set notation for corresponding setsYou, mean Last edited by anonimnystefy (20131019 00:42:44) The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #6 20131019 01:12:16
Re: Set notation for corresponding setsYes, thank you. but I knew what you meant. Last edited by Reuel (20131019 01:17:14) #7 20131023 04:20:07
Re: Set notation for corresponding setsOkay, here is what I have. I would appreciate any edits or suggestions anyone who knows sets or mathematical writings might have to offer to help improve the quality of what I have so far. [in that it might be said to go from ±∞], the set T might be written so as to contain some boundary condition so that it can be rewritten as ; but if we further define the set as being of certain relevance to only that boundary condition Z, we say let so as to be redefined as . Suppose then we have a series of events in time that are also restricted to Z (which is actually what I intend to be the reason for why Z is a boundary condition in the first place) and let that ordered set (ordered because it corresponds to time T) be given by . Because every event in E corresponds to no more and no less than one event in T, (meant to read: a function t is the mapping of the set E to the set T such that for all t's in the set T there exists one and only one e in E such that t as a function of e is equal to t) such that for a bijector J between T and E, so that and that is, the cardinality of both sets is equal such that the magnitude of both sets is equal: .  Thank you for any and all input. Any and all critiques and edits are welcome. P. S. Yes, starting out with the most fundamental definition of time is a goal, then to be worked out so as to be limited to the specified boundary condition which is sobounded because of the set of E being the only set where T is relevant. 