taryneast comments on Artificial Addition - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (117)
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).