Editing Addition (section)

=== Combining sets ===
[[File:AdditionShapes.svg|right|thumb|upright=0.8|One set has three shapes while the other set has two. The total of shapes is five, which is a consequence of the addition of the objects from the two sets: <math> 3 + 2 = 5 </math>.]]
Possibly the most basic interpretation of addition lies in combining [[Set (mathematics)|sets]], that is:{{sfnp|Musser|Peterson|Burger|2013|p=[https://books.google.com/books?id=8jh7DwAAQBAJ&pg=PA87 87]}}
{{blockquote|When two or more disjoint collections are combined into a single collection, the number of objects in the single collection is the sum of the numbers of objects in the original collections.}}
This interpretation is easy to visualize, with little danger of ambiguity. It is also useful in higher mathematics (for the rigorous definition it inspires, see {{Section link||Natural numbers}} below). However, it is not obvious how one should extend this version of an addition's operation to include fractional or negative numbers.<ref>See {{harvtxt|Viro|2001}} for an example of the sophistication involved in adding with sets of "fractional cardinality".</ref>

One possible fix is to consider collections of objects that can be easily divided, such as pies or, still better, segmented rods. Rather than solely combining collections of segments, rods can be joined end-to-end, which illustrates another conception of addition: adding not the rods but the lengths of the rods.{{sfnp|National Research Council|2001|p=[http://books.google.com/books?id=pvI7uDPo0-YC&pg=PA74 74]}}
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