0
votes
0answers
7 views

Upper bound on cardinality of a field [migrated]

Is there an upper bound on the cardinality of a field? The "biggest" fields I know are the field of real numbers, or the field of complex numbers. Is there a field with cardinality greater than ...
7
votes
2answers
479 views

Is there one binary operation foundational for set theory?

The membership relationship "$\epsilon$" is foundational for set theory, in the sense that the axioms of any set theory are formulated in the language of "$\epsilon$". Naturally, the question arises ...
-1
votes
1answer
153 views

Algebra generated by a tree [Edit] [closed]

Suppose that $(T,\leq)$ is a partially ordered set, we say $T$ is a tree* if for every $i\in T$, $\{s: s\in T, s\leq t\}$ is a well-founded chain. What I need to know is: Can the algebra ...
0
votes
0answers
103 views

Operating on a set of sequences - such as adding sequences and so on possible even when sequence is coded as number?

From http://math.stackexchange.com/questions/346680/operating-on-a-set-of-sequences-such-as-adding-sequences-and-so-on-possible-ev Suppose that there is a way to code some set of sequences into ...
8
votes
4answers
631 views

Groups and rings which are not sets

An algebraic structure such as a group, ring, field, etc. is usually defined to be a set with some operations satisfying certain properties. I am curious what, if anything, goes wrong when the ...
1
vote
1answer
917 views

Cardinality of symmetric group [duplicate]

Possible Duplicate: Cardinality of the permutations of an infinite set Why does the symmetric group on an infinite set X have the cardinality of the power set ${\cal P}(X)$?