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Small Numbers: The child who merely follows a mechanical rule of thumb, gets lost easily when the going becomes at all rough. It is much better for him to understand addition, for example, "as a mathematical way of treating numbers when we want an answer to a particular question: 'How many (much) in all?' or 'What is the total?' " He should know that the sum is always larger than the separate numbers, except when zero is added—and understand why this is so. A meaningful method of learning arithmetic is based on insight into the structural relations of numbers.
The thickness of sheet iron and steel is denoted by a system of arbitrary gage numbers. The numbers in use differ for different products. On March 3, 1893, the United States Congress passed an act establishing a standard gage for sheet and plate iron and steel for use by the customs service. In this system the gage numbers indicate thickness, or the weight per unit area. Sizes of wire are also denoted by a special system of arbitrary gage numbers.
Although in the long run the commercial revolution laid the basis for the prosperity of small numbers, intensively cultivated farms in the 5th century B. c., the immediate effects on the small numbers farmer were disastrous. The general economic dislocation that accompanied the transition from subsistence to specialized farming caused an agricultural crisis, and the only solution offered by the new money economy was usury. The small numbers farmers were forced to borrow on the Security not only of their lands, but also of their persons, and, as a result, large numbers were threatened with reduction to the status of sharecropping serfs. |
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