Can you define an ordered set using something like Kurwatowski's definition of ordered pairs?
pls responds
>>7904313
Who is she?
>>7904624
she's old now, like 30 years old
Very old
Too old
>Kurwatowski
remove this, I ask you kindly
>>7904873
merely a typo :&)
Any poset? I think not. Linearly ordered set? Yes
>>7904890
how
>>7904624
Rose Wolfe, newfriend
>>7904624
>she
>>7904313
I guess that you're thinking the ordered pair (a,b)={{a},{a,b}} as a poset using the order given by x<y iff x belongs to y so your idea is to find for every poset (X,<) a set A such that with the order given by x<y iff x belongs to y the poset A turns to be isomorphic to (X,<).
If what I just said is what you want then you can use the Von Neumann definition of ordinal number to find for every well ordered set the set A with the property, for a general poset (or even a general linearly ordered set) I have no idea if the set A exists.
Maybe >>7904890 can help in the linearly ordered case.
>>7904313
she has the face of cumberbatch
>>7905286
>>she
>what is the meaning of this statement
Could you make it any more obvious?
>>7905286
fuck off rose is an pure maiden
>>7904313
>Kurwatowski
Ty downie jebany
how is rose becoming a sci meme in 2016
>>7905561
Rose is /sci/
>>7904313
source?
>>7904313
Who is this scrotum totem?
>>7904313
>>7907455
Obviously? The set of all [math] \{\{x\}, \{x,y\}\} [/math] such that [math]x<y[/math] encodes the order. After all, as you said, [math]\{\{x\},\{x,y\}\} [/math] can be taken as a definition of [math](x,y)[/math].
>>7907458
I think you misread the question. I'm talking about defining ordered sets/lists by extending {{x},{x,y}}.
>>7905266
For a total order you can just use [math]\{ \{ x \in X | x \le y\} | y \in X \}[/math].
>>7907521
Actually make that [math]\{ \{ X_i | i \in I \land i \le j\} | j \in I \}[/math] where [math]I[/math] is the totally ordered index set. For pairs, [math]I[/math] would be [math]\{1, 2\}[/math].
And I guess I need to think about whether this would have the expected properties.
>>7907521
>x <= y
I don't get it
>>7907537
>And I guess I need to think about whether this would have the expected properties.
Starting with whether the mapping from functions of [math]I[/math] to these things is injective.
"define an ordered set using"
Can you please say clearly what you're asking?
>>7907463
Well, that's pretty vague, but probably anything that would be sufficiently "like" Kuratowski would work only for well-ordered sets.
Certainly, the natural generalization [math] \{ \{x \} , \{x,y \}, \{x,y,z\}, \ldots \} [/math] (potentially extended transfinitely) can code only well-ordered sets.
>>7907541
Underrated.
