bruto
Penultimate Amazing
Iacchus, I was tired last night (long drive home from airport, etc.) and missed one last point with regard to sets and subsets, which I hope I can convey in a way that makes sense, though at this point I somehow doubt it will make a difference. Anyway, I think you have the concept of sets and subsets backwards, and have not yet grasped what a subset is.
A set is a logical construct, which consists of an unordered group of things which share some common characteristic which the set names. All members of the set must possess that characteristic. If they do not they are not members of the set. Members of the set can be individual objects, or other sets, which in relation to the set in question are called subsets.
A subset is a portion of that group, distinguished by sharing some ADDITIONAL characteristic that is NOT shared with the rest of the group. (this is a bit of an oversimplification, since by definition a subset can consist of the entire set, but perhaps the addition of the qualifier "identity" can count as an additional characteristic)
A subset is NOT a group that shares some but not all of the characteristics defining the larger set. Please read this sentence with care, Iacchus, and do not proceed until you have comprehended it.
You can make a set of anything you want. All you need to do is name the rule that qualifies inclusion. In the set of "things that are black and white" I might put a newspaper, the movie Citizen Kane, a nun and the Linux penguin, and as a subset I could put the set of all striped skunks. The set of all striped skunks is a subset of black and white things, because in addition to being black and white, they share other characteristics that are not named in the definition of the set "black and white." Not all black and white things are mammals, for example, nor are all mammals carnivorous, etc. etc. In each case of forming a subset, you will notice that I am adding characteristics, not subtracting them. I could not put, as a subset, the set of all crows. Crows are black, but not black and white. Possession of some but not all of the characteristics of the set is not what makes a subset. Possession of some, but not all, of the characteristics of the set makes an object not a member of the set at all.
If you take a can, and a quantity of soup, you can make a set out of it. It is the set of things which are either soup or cans. To be a member or a subset of that set a thing must be either a can or soup or both. The set "can of soup," being both, is a subset of this larger set. The can is not a subset of the can of soup, and the soup is not a subset of the can of soup.
Adding definition to a set makes it less inclusive, not more.
OK. That's it. I'm tired of sets. If you cannot accept or understand the idea by now, too bad. But your arguments will be junk if you arbitrarily redefine terms to mean something that they do not.
A set is a logical construct, which consists of an unordered group of things which share some common characteristic which the set names. All members of the set must possess that characteristic. If they do not they are not members of the set. Members of the set can be individual objects, or other sets, which in relation to the set in question are called subsets.
A subset is a portion of that group, distinguished by sharing some ADDITIONAL characteristic that is NOT shared with the rest of the group. (this is a bit of an oversimplification, since by definition a subset can consist of the entire set, but perhaps the addition of the qualifier "identity" can count as an additional characteristic)
A subset is NOT a group that shares some but not all of the characteristics defining the larger set. Please read this sentence with care, Iacchus, and do not proceed until you have comprehended it.
You can make a set of anything you want. All you need to do is name the rule that qualifies inclusion. In the set of "things that are black and white" I might put a newspaper, the movie Citizen Kane, a nun and the Linux penguin, and as a subset I could put the set of all striped skunks. The set of all striped skunks is a subset of black and white things, because in addition to being black and white, they share other characteristics that are not named in the definition of the set "black and white." Not all black and white things are mammals, for example, nor are all mammals carnivorous, etc. etc. In each case of forming a subset, you will notice that I am adding characteristics, not subtracting them. I could not put, as a subset, the set of all crows. Crows are black, but not black and white. Possession of some but not all of the characteristics of the set is not what makes a subset. Possession of some, but not all, of the characteristics of the set makes an object not a member of the set at all.
If you take a can, and a quantity of soup, you can make a set out of it. It is the set of things which are either soup or cans. To be a member or a subset of that set a thing must be either a can or soup or both. The set "can of soup," being both, is a subset of this larger set. The can is not a subset of the can of soup, and the soup is not a subset of the can of soup.
Adding definition to a set makes it less inclusive, not more.
OK. That's it. I'm tired of sets. If you cannot accept or understand the idea by now, too bad. But your arguments will be junk if you arbitrarily redefine terms to mean something that they do not.
