It's only a formal (i.e. symbolic) sum, understood as an element of the $\mathbb R$-module generated by the simplexes $\sigma_i$ (similar to vectors from a basis in linear algebra), where addition is by definition component-wise, commutative and distributive. It does not possess a clear geometrical meaning. In particular it does not represent a map into $M$. Try to look for references on singular homology.

What does a singular simplex with real coefficient mean 
I have a simple question (I think) that I'm not making much progress finding an answer to with Google.  I have a structure as follows:

/// &lt;summary&gt;
/// A class to represent the sync settings for a single camera.
/// &lt;/summary&gt;
public class CameraSyncSettings
{
    public string ID { get; set; }
    public string SyncPath { get; set; }
    public bool OverwriteExisting { get; set; }
};


And then an array of these in the program, one for each camera:

List&lt;CameraSyncSettings&gt; MyCameraSettings = new List&lt;CameraSyncSettings&gt;();


Now, what I want to do is have a property in my settings such that I can read/write this array into it to persist the information between sessions. 

How can I do this and what is the best/most efficient way?
