- #36
Hurkyl
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No, I am not. As I said, - refers to additive inverse, and / refers to multiplication by the multiplicative inverse.manker said:I don't quite follow this. By -1/9 I take it you are denoting the number that could also be represented as the recurring decimal -0.1111 ...
The additive inverse of 1 is ...999. (Because ...999 + 1 = 0)
The multiplicative inverse of 9 is ...8889. (Because ...8889 * 9 = 1)
Finally, ...999 * ...889 = ...111.
As I had said, the numbers in this number system are the left-infinite strings of decimal digits. -0.111... doesn't denote a number.
The simplest is to define the phrase "The limit of ____ as __ approaches [itex]\infty[/itex]" as a whole; the individual symbols and words aren't given any meaning. This is something you'd probably see in an elementary calculus book.I'm also wondering what number the symbol oo (infinity) represents (if any). What does it mean when we say 'as x approaches oo' ?
A slightly more sophisticated treatment would define a new number system (such as the extended real numbers or the extended natural numbers) that contains an element called [itex]+\infty[/itex], and then you can just use the ordinary definition of the phrase "The limit of _____ as __ approaches __".