ordinal

  1. ISP

    Enumerating An Uncountable Ordinal

    Disclaimer: I have a sense of humor and a purpose, so I’m going to try and enumerate $\omega_1$ itself. Clearly that is a crankish proposition, so this disclaimer is meant to clarify what I mean to accomplish and acknowledge that there should obviously be an error if I conclude that I have...
  2. G

    Ordinal Arithmetic

    Problem Statement: Show that the set X of all ordinals less than the first uncountable ordinal is countably compact but not compact. Let μ be the first uncountable ordinal. The latter question is easy to show, but I stumbled upon a curiosity while attempting the former. In showing the...
  3. C

    Bidimensional Ordinal

    Can anoyone let me write an example of a Bidimensional Ordinal ? Thanks Ciao Stefano
  4. C

    VON NEWMANN's ORDINAL

    It's possible to write the Von Newman's Ordinal with a funny formula: \begin{tabular}{lll} 1 0 0 2 0.1 0.1 3 0.02 0.12 4 0.003 0.123 5 0.0004 0.1234 6 0.00005 0.12345 Till 9 (to go general the formula must be...
  5. W

    monotonic laws for ordinal subtraction

    I have to prove some monotonic laws for ordinals. It's quite comfortable for me to show monotonic laws of ordinal addition (e.g. $\beta\leq\gamma\Rightarrow\alpha+\beta\leq\alpha+\gamma$). But when it comes to laws with subtraction, then I'm not sure where to start. Maybe it's because of...
  6. V

    Finding the Median with Categorical Data

    How do you find the median within Ordinal data if you are looking at education levels and their distribution as below?: High School: 7 ppl Some College: 11 ppl College Graduate: 14 ppl I understand how to get the median for numerical data of an even sample size where you take the average of...
  7. S

    Significance test for ordinal data (Kendall Tau)?

    I have a litte problem I'm trying to figure out. I have a set of 4 variables, with an output value, and I want to see if these variables have any affect on the output as I we add them. I'll try to explain more in depth: We'll set the output as Y, which we call a quality measure. The higher the...
  8. X

    ordinal, uniqueness question

    For any ordinal \alpha < \omega^N, there are unique n<N, x< \omega, \beta < \omega^n such that \alpha=\omega^n \cdot x + \beta. Hint: Choose n largest such that \omega^n \leq \alpha, and x largest such that \omega^n \cdot x \leq \alpha. I do not see how to use the hint to prove this. Would the...
  9. R

    ordinal arithmetic

    Hello. Definition: a,b are ordinals and a\leq b. Then there exists a unique c such that a+c=b. We write c=b-a. Show that this subtraction definition coincides with the following operation defined by recursion: (1) a-a=0 (2) (b+1)-a=(b-a)+1 for a <= b (3) c-a = \text{sup}\{b-a:b<c\} when c...