Math / Logic Discussion

[Strikingwolf]

That's what globals are for.

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*dies*

I think we need access to the "beyond" from "A Fire Upon The Deep" to really understand those infinite sums.

(just stay away from the "transcend" ...)

*dies again*

And there are ways to understand the infinite sums, such as these

same idea as understanding why e^(i * pi) = -1 on an intuitive level (not a proof level)

*cool videos are cool*

 

[Lethosos]

Well, in terms of code, globals make great absolutes as long as they're correct in the first place. (Especially when "constant" is invoked.)

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[Strikingwolf]

Well, in terms of code, globals make great absolutes as long as they're correct in the first place. (Especially when "constant" is invoked.)

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Specific modules for constants FTW

 

[Lethosos]

I just noticed something--there's a good reason why a computer can't test the initial theorem posited in this thread. Primarily, we can't give it an infinite set of data due to there being a hard limit on the amount of data we can give it.

This is why recursive functions, coded right, always has a way to break or step out of itself.

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[Strikingwolf]

I just noticed something--there's a good reason why a computer can't test the initial theorem posited in this thread. Primarily, we can't give it an infinite set of data due to there being a hard limit on the amount of data we can give it.

This is why recursive functions, coded right, always has a way to break or step out of itself.

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That's actually wrong there are many programming languages that allow lazy data. For example, in Haskell I can represent the list of all Fibonacci numbers like so

fibs = 0 : 1 : zipWith (+) fibs (tail fibs)

The problem with this is that it usually has to have some relation to the previous values. However, if you generated the values randomly this would not be the case, and you would find that one of them was false. Solving this problem is pretty much equivalent to solving the halting problem for this Haskell program

import System.Random

main = do
  gen <- newStdGen
  let ns = randoms gen :: [Int]
  any (\x -> x `mod` 2 == 0) ns

or in pseudocode

ns = infinite list of random integers
any n in ns where n % 2 == 0