Interchange station for a variety of parallel lines
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Latest Posts by middlering - Page 3
blood is not kosher
assuming vampires breathe, and are therefore alive, what do they do
Generalized Golf
I have looked up nothing about golf to write this.
Let C be any topological space. We will call this the ‘course’. For any two points x,y ∈ C we have a collection S_xy of ‘shots from x to y’, where each ‘shot’ s ∈ S_xy is a path in C from x to y, which is to say a continuous function s: [0,1] → C with s(0) = x and s(1) = y. For a shot s ∈ S_xy we call x its ‘start’ and y its ‘end’. Let S denote the collection of all shots in C between any two points.
A ‘hole’ on C is a triple (t,h,p) where t ∈ C is a point called the ‘tee’, h ⊂ C is a subset called (confusingly) the ‘hole’, and p is an ordinal number called the ‘par’. For any cardinal number κ we define a ‘golf’ of length κ to be a function g: κ → H, where H is a set of holes on C. A golf g is called ‘finite’ if κ is finite and the par of every hole in the image of g is finite. We define the par of a finite golf as the sum of the pars of its constituent holes.
A quintuple (C,S,κ,H,g) defined like above is called a ‘game of (generalized) golf’.
Take a hole (t,h,p), a successor ordinal ω+1. Let F: ω+1 → S be a function such that F(0) is a shot from t, for every i < ω the end of F(i) equals the start of F(i+1), the end of F(ω) is an element of h, and no F(i) ends in h before this. Such an F is called a ‘play’. We call ω the ‘score’ of F.
A ‘golfer’ is a collection of probability spaces, which for any shot s ∈ S with start x and end y gives a probability space on the set of shots from x. This is to be interpreted as the ways in which a shot can deviate from the golfer’s intent.
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Now to define the real numbers by way of games of golf on ℚ.
HAPPY 2024 YALL WE'RE CELEBRATING WITH THE SAPPHICS EVER
2023 was crazy but also i don't remember most of it Imao, I genuinely hope yall had a good year though and made some accomplishments (whether or not they were what you wanted in the beginning of the year) and I hope 2024 is a great year for you all!!!! 🥳💜🎉
Happy 2025!
I worked like mad to finish this but here it is – some insanely large number of words about the year that was, through the lens of Billy Joel songs with "night" in the title because they are fascinating as all get out.
Special shoutout to @thebreakfastgenie for helping to infect me with the urge to go even deeper into the old man research.
if you’re a new tumblr user from tiktok or IG or something and only like posts and dont reblog them yeah people will think you’re a bot and block you but you will also make this website actively worse. they want “algorithmic” users like you, served recommended posts through likes, not people who just follow each other and respond to the direct chronological feed. there is a reason this website is still better than the rest, even with all its problems, do not ruin this