Adding 0 to 1: What is the Sum?

[whozum]

Well, it isn't a clear cut question. The first thing to have asked yourself is: *how* do you try to sum all the numbers between 0 and 1. That is to say that there really was a more basic question going on. For instance it *is* possible to sum more than a simple series indexed by the natuarl nubmers.

eg, let w be a symbol and r run from 1 to infinity, then define x(w)_r to be a geometric series of positive terms that sums to 1/2, then x(2w)_r be one that sums to 1/4, then x(3w)_r be oen that sums to 1/8, and so on so that the sequence x(nw)_r sums to 1/2^n

then i claim that this is gives a series indexed by the ordinal w^2 (or something like that) whose sum which we do transfinitely is 1.

However [0,1] is uncountable. so we can't do this. So, it is perfectly reasonable to ask how you thought the sum was going to be taken.

The thought that crossed my mind, in the shower might I add, was that there are a bunch of numbers between 0 and 1, an infinite number of them. If I added them all, do they converge, and if so what do they converge to.

The simplest way to reflect that was to ask it the way I did. Arildno says that my question implies that I'm asking about integers, which is in all honesty a mockery.

It was a 5 second ordeal that was answered in the first 3 posts.

 

[matt grime]

Why is it a mockery? You ask a question that makes no sense, so others must attempt to make sense of it. Arildno demonstrated that the question as posted makes no sense by posting one interpretation that shows highlights the absurdity (in the non-insulting sense) of the situation.


"number" is a vague fuzzy term that could mean anything. natural nubmer, whole number, rational number, real nubmer, complex number. Only context makes it make sense, and there is no context for adding up all real numbers (or rational ones for that matter) between 0 and 1.