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Dimension
The dimension of an array is the number of indices that you need to use to specify a cell. A one-dimensional array only requires one number, where as an n-dimensional array requires n indices.
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Modeling
The process of taking a some structure, such as a game board, and using some other form to represent it, such as an array.
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Two-Dimensional
A two-dimensional array is an array where each cell is specified by two indices, often thought of as a row and column.
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Multi-Dimensional
Refers to arrays being more than one-dimensional.