you can tell i didnt copy paste it because i only had the patience to type two words
why are letters like this
ω
thats not epsilon by the way thats still omega
nyaaaaaaaaaa yeah that gets used for infinity in some contexts nya nya nya
I found a youtube video about Mate in ω on an infinite chessboard
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why are letters
no thats not letters thats people
isnt this just having both kings left
good video (it gave a sane motivation for infinite ordinals)
Angular velocity…
getting checkmate never and checkmate in an indefinite amount of time is functionally the same thing yet theoretically different and i hate that
…i almost failed mathematics
no
on a finite chessboard, Mate in ω isn’t possible
But on an infinite chessboard, you can get strange positions
Suppose it’s black to move, and white is threatening mate. Also suppose that black can defend mate by moving back their rook N spaces (for any N), and then white will be able to force mate in N moves after that (and assume black has no better defense) (you can construct positions to have these properties)
So, while it’s still black to move, white has forced mate - but we can’t say White has forced mate for any finite number… so we come up with a new ordinal number, ω, which is greater than all finite ordinals
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thanks
nyaaaaaaa these are different! one of them will eventually happen!
video if you’re interested
IN AN INFINITE AMOUNT OF TIME IS LOGICALLY THE SAME AS NEVER
infinity is neverending!!
not an infinite amount of time. an arbitrarily large amount of time.
im killing john maths