@MoralOfStory @argletargle Computing with, say, sqrt(2) is actually pretty easy.
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Replying to @tailcalled
@tailcalled@argletargle I'll wait here while you compute the entire number. ...1 reply 0 retweets 1 like -
Replying to @MoralOfStory
@MoralOfStory@argletargle Just represent it symbolically, i.e. a + b sqrt(2). Why privilege the fraction/decimal representation?1 reply 0 retweets 1 like -
Replying to @tailcalled
@tailcalled@argletargle That's manipulating the programs which produce the numbers, and I don't claim you can't do that.1 reply 0 retweets 0 likes -
Replying to @MoralOfStory
@MoralOfStory@argletargle I'm not sure I understand the problem. What properties must a representation have before it counts?1 reply 0 retweets 0 likes -
Replying to @tailcalled
@tailcalled@argletargle I'm using "numbers" to denote the sequence of digits. In my view, math notation is a program to produce the digits.2 replies 0 retweets 0 likes -
Replying to @MoralOfStory
@MoralOfStory@argletargle Why? Digits are not exactly well-behaved...1 reply 0 retweets 0 likes -
Replying to @tailcalled
@tailcalled@argletargle I believe that's my point :)1 reply 0 retweets 0 likes -
Replying to @MoralOfStory
@MoralOfStory@argletargle Oh. I thought your point was that no-one had done an exact&general calculation on reals/computable reals.2 replies 0 retweets 0 likes -
Replying to @tailcalled
@MoralOfStory@argletargle e.g. you can't, in general, compare two computable reals for equality.1 reply 0 retweets 0 likes
@tailcalled @argletargle Yes, because that involves examining the actual digits, i.e., executing the programs all the way to the end
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