Less Wrong is a community blog devoted to refining the art of human rationality. Please visit our About page for more information.

Misha comments on Artificial Addition - Less Wrong

36 Post author: Eliezer_Yudkowsky 20 November 2007 07:58AM

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Comments (117)

Sort By: Old

You are viewing a single comment's thread. Show more comments above.

Comment author: [deleted] 31 December 2010 02:47:38AM 1 point [-]

You have a point. I tend to dislike arguments about mathematics that start with "well, this definition is just a choice" because they don't capture any substance about any actual math. As a result, I tried to head that off by (perhaps poorly) making a case for why this definition is a reasonable choice.

In any case, I misunderstood the nature of what you were saying about the convention, so I don't think we're in any actual disagreement.

I might also turn that argument back on you and repeat what I said before: "if you meant 2, why not just say 2?"

If I meant 2, I would say 2. However, our system of writing repeating decimals also allows us to (redundantly) write the repeating decimal 1.999... which is equivalent to 2. It's not a very useful repeating decimal, but it sometimes comes out as a result of an algorithm: e.g. when you multiply 2/9 = 0.222... by 9, you will get 1.999... as you calculate it, instead of getting 2 straight off the bat.

Comment author: taryneast 31 December 2010 09:02:15AM 1 point [-]

You have a point. I tend to dislike arguments about mathematics that start with "well, this definition is just a choice"

Me too! Especially as I've just been reading that sequence here about "proving by definition" and "I can define it any way I like"... that's why I tried to make it very clear I wasn't saying that... I also needed to head of the heading off ;)

Anyway - I believe we are just in violent agreement here, so no problems ;)