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

taryneast 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: taryneast 30 December 2010 12:15:17PM *  -2 points [-]

1.999... does not equal 2 - it just tends towards 2

For all practical purposes, you could substitute one for the other.

But in theory, you know that 1.9999... is always just below 2, even though it creeps ever closer.

If we ever found a way to magickally "reach infinity" they would finally meet... and be "equal".

Edit: The numbers are always going to be slightly different in a finite-space, but equate to the same thing when you allow infinities. ie mathematically, in the limit, they equate to the same value, but in any finite representation, they are different.

Further Edit: According to mathematical convention, the notation "1.999..." does refer to the limit. therefore, "1.999..." strictly refers to 2 (not to any finite case that is slightly less than two).