Tagged Questions

31 views

Could someone check this proof for me?

The problem (and a definition first): The following definition explained Let $U \subseteq \mathbb{N}$. We say that a function $x: \{0,1\}^U\to \{0,1\}$ is a $xor$ on the set $U$ if the following ...
21 views

$( A,\le)$ and $(A',\le')$ are partially ordered sets. A map $\phi : A \to A'$ is called order preserving from $(A, \le)$ to $(A', \le')$ if for all $x, y \in A : x \le y \implies \phi(x) \le' ... 1answer 56 views What is the terminology for this type of order-preserving function? As I roughly know, a function$f$in$\mathbb{R}$is called order-preserving if$f(x)>f(y)$for$x>y$,$x,y \in \mathbb{R}$. May I ask, if anybody knows the terminology for two functions$f$... 0answers 37 views Using transfinite induction to prove that an order preserving bijection is the identity function [duplicate] Let$(W,\le)$be well ordered. If$f:W\to W$is an order preserving bijection, using transfinite induction how do I prove that$f$is the identity function on$W$? I am weak when it comes to solving ... 0answers 87 views Why are complete lattice homomorphisms defined that way? Given a function$f : X \rightarrow Y$and a set$A \subseteq X$, there's at least two possible ways of interpreting the direct image$f(A),$as explained here. In the notation of that question, write ... 1answer 131 views Total orders making a family of functions non-decreasing Suppose$S$is a finite set and we are given a family of functions$(f_i:S\to S)_{i\in I}$. When can we find a total order$<$on$S$such that all the functions$f_i$are nondecreasing? I am ... 0answers 140 views From point-wise to essential supremum of a set of real-valued measurable functions I want to prove some property about essential suprema and I think I can show them for the pointwise supremum$\sup S$. The problem is, that the sets involved are uncountable and thus, the point-wise ... 2answers 182 views Well-Ordered Sets and Functions I need some assistance with the following problems. I've come up with some ideas but may need some clarification. 1) Let$S$be a well-ordered set. a) Need to show$S$has a first element. ... 2answers 113 views Continuation of strictly monotone functions on$\mathbb{R}$While studying the properties of ordinal utility functions, I came across the following question. Given a strictly increasing function$f : D \rightarrow \mathbb{R}$, where$D$is an arbitrary ... 2answers 75 views Can such a function exist? Denote by$\Sigma$the collection of all$(S, \succeq)$wher$S \subset \mathbb{R}$is compact and$\succeq$is an arbitrary total order on$S$. Does there exist a function$f: \mathbb{R} \to ...
This is my problem: For every couple of integers $(a,b)\in\mathbb{Z}\times(\mathbb{Z}\backslash\{0\})$ we denote with $r(a,b)$ the remainder of the division between $a$ and $b$. Consider the ...
While playing around with least-fixed-point constructions on a powerset lattice, I've found this property to be useful. Let's say that $F : \mathcal{P(U)} \to \mathcal{P(U)}$, and that \$A \subseteq ...