
The strange non-transitivity of random variables (2014) - throwaway000002
https://www.andreasleiser.com/blog/?p=186
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brudgers
Related, Non-transitive dice:
[https://en.wikipedia.org/wiki/Nontransitive_dice](https://en.wikipedia.org/wiki/Nontransitive_dice)

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mtdewcmu
That is neat and a lot easier to understand than the original link. All the
notation made my eyes glaze over.

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hebdo
While Kolmogorov's definition of probability looks a bit spooky at first, I
definitely recommend going through it at some point. Not only it feels nice,
it also makes understanding probabilistic concepts easier (e.g. understanding
that a statistical space is simply a "lifted", or rather parametrized, version
of a probabilistic space).

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danharaj
> Examples of binary relations are binary operations (like +,–,⋅,/) on
> N,Z,Q,R,C,Rn, … etc. (where defined), since functions are special cases of
> relations, or, the order relations <,≤,>,≥ on R, for instance.

A function of two variables is a ternary relation, not a binary relation.
/pedant

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x3n0ph3n3
Last I checked, binary implies 2 and ternary implies 3. There are 2 inputs,
therefore it's a binary relation or operator.

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danharaj
Idk what to tell you other than that you should check the definitions. A unary
function is a special case of a binary relation and in general an n-ary
function is a special case of a n+1-ary relation.

Edit - Maybe this clarifies it: When we talk about a function we designate one
of its variables as the 'output' and talk about its arity in terms of the
inputs. When we talk about a relation there is no distinguished output: A
relation is a fully symmetrical definition. That's why the arity of a function
is one less than the arity of that same function thought of as a relation
between its inputs and output.

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quietplatypus
this isnt paradoxical at all, it's just you are looking at only 2 dice at a
time not the full joint probability of a < b < c. i can come up with similarly
retarded "paradoxical conclusions" if i took enough samples of different tiny
slices of things.

dude is just trying to sound smart with yet another "counterintuitive
probability post"

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jeffsco
Imagine a tournament to choose the best tennis player. If you imagine these
dice as a simple model of a tennis player, there can be no best tennis player.
So tennis tournaments make no sense. This is paradoxical if you believe in
tennis rankings.

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quietplatypus
Uhh, what if I told you that like most people with common sense and who
realize that the initial conditions of a tournament are fixed in advance and
that the ranking at the end only applies for that tournament and there are
many other factors that influence who wins and loses in each match, I take
tennis rankings with a grain of salt?

Hell I can even accept that player A > B > C > A if each has different skills
and specialities that they bring to the table, without trapping myself and
others into declaring it's some "paradoxical nonsense". Do we say rock < paper
< scissors < rock and declare it's the end of mathematics?

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rumbo
Does anyone anywhere say that if something may appear to some people
paradoxical (have you ever thought about what paradoxical means?) it is the
end of mathematics?

