# ordinal

1. ### Enumerating An Uncountable Ordinal

Disclaimer: I have a sense of humor and a purpose, so Iâ€™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. ### 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 Î¼ 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. ### Bidimensional Ordinal

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