Class (set theory)
In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share. Some classes are sets, for instance the class of all integers that are even, but others are not, for instance the class of all ordinal numbers or the class of all sets. Classes that are not sets are called proper classes.A proper class cannot be an element of a set or a class and isn't subject to the Zermelo-Fraenkel axioms of set theory; thereby a number of paradoxes of naive set theory are avoided. Instead, these paradoxes become proofs that a certain class is proper. For example, Russell's paradox becomes a proof that the class of all sets is proper, and the Burali-Forti paradox becomes a proof that the class of all ordinal numbers is proper.
The standard Zermelo-Fraenkel set theory axioms do not talk about classes; classes exist only in the metalanguage[?] as equivalence classes of logical formulas. Another approach is taken by the von Neumann-Bernays-Gödel axioms[?]; classes are the basic objects in this theory, and a set is then defined to be a class that is an element of some other class. The proper classes, then, are those classes that are not elements of any other class.
Several objects in mathematics are too big for sets and need to be described with classes, for instance large categories or the class-field of surreal numbers.
The word "class" is sometimes used synonymously with "set", for instance in the term "equivalence class".
I'm going to take her with me.
BIGELOW--[Surprised.] On the Asian expedition?
CURTIS--Yes. I haven't told her yet but I'm going to to-day. It's
it's not too late yet.
CURTIS--[With a grin.] Thirty-nine candles, if you're/re.html">re/re.html">re/re.html">re thinking of
Curt.
CURTIS--[Disgustedly.] You talk like an old woman, Big. What have
[There is a knock at the door and MARTHA's voice calling: "May I
MARTHA enters. She is flushed, excited, full of the joy of life,
governess. They're too active for me. [She throws herself on the
Martha. [BIGELOW looks embarrassed.]
MARTHA--[Laughing at him.] Well, I declare! Of all the horrid
prevaricates, Mrs. Jayson.
MARTHA--There now, Curt! I'm sure it was you who said it. It
despite your husband's calumny. May your shadow never grow less!
MARTHA--Thank you. [She shakes his proffered hand.html">hand heartily.]
BIGELOW--And now I'll collect my flock and go/go.html">go home.
CURTIS--So long, Big. Be sure you don't mislay one of your heirs!
BIGELOW--No fear--but they might mislay me. [He goes. CURT sits
after a pause, waving her hand.]
MARTHA--There they go. What darlings they are! [CURTIS grunts
couch--with a sigh.] Whoever did say it was right, Curt, I am
No. I feel it.
CURTIS--[Puts his arms around her protectingly.] Nonsense! You're
dear. Even you. [She touches the white hair about his temples
you're asleep some time--and then nobody'll know.
CURTIS--[Looking at her.] You haven't any silver.
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