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In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system. The decimal multiplication table was traditionally taught as an essential part of elementary arithmetic around the world, as it lays the foundation for arithmetic operations ...
Zeroes may be written in or left blank. This does not affect the operation of the device. The triangle in the bottom left of the table is always blank. The following diagram shows the multiplication table for the simple 7: Napier's Promptuary: multiple diagram for digit 7
Multiplication by a positive number preserves the order: For a > 0, if b > c, then ab > ac. Multiplication by a negative number reverses the order: For a < 0, if b > c, then ab < ac. The complex numbers do not have an ordering that is compatible with both addition and multiplication. [30]
The group {1, −1} above and the cyclic group of order 3 under ordinary multiplication are both examples of abelian groups, and inspection of the symmetry of their Cayley tables verifies this. In contrast, the smallest non-abelian group, the dihedral group of order 6, does not have a symmetric Cayley table.
The table above (even if some more columns are added) maintains one line per country for narrower browser and screen widths. So it is therefore more readable and scannable in long country tables. The table format below can greatly increase in number of lines, and require more vertical scrolling, especially if more columns are added.