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'addition'
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| Title of object: |
addition |
| Canonical Name: |
Addition |
| Type: |
Definition |
| Created on: |
2007-01-17 18:08:43 |
| Modified on: |
2007-01-20 13:19:34 |
| Classification: |
msc:11B25, msc:00A05, msc:00A06 |
Revision comment (for changes between this and next version):
| Changes for correction #11277 ('addition'). |
Preamble:
% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands here
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Content:
{\em Addition} is a mathematical operation in which two or more numbers are added up. The numbers may be real, imaginary or complex. Two examples: 2 + 2 = 4; $4 + \pi \approx 7.14159$. In the realm of real numbers, adding up positive numbers yields a result that is greater than any of the summands.
The usual operator is the cross with its four arms of equal length pointing north, east, west and south: +. This operator is used in standard infix notation as well as in Polish notation and reverse Polish notation. Regardless of the order of the operands, addition is commutative: $x + y + z = x + z + y = y + x + z,$ etc.
The iterative operator is the Greek capital letter sigma, e.g., $$\sum_{i = 1}^n i^3.$$ Because of the aforementioned commutativity, it doesn't matter if the iterator is started at the smallest value or the largest value.
Besides the possibility of overflow, addition presents no problems for fixed point arithmetic provided the operands are representable in fixed point to begin with. In floating point there exists the possibility of loss of precision (if for example we were to add up several different irrational numbers). |
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