Mathematical processes can lead to a kind of model of a thing, from which insights can be gained about the thing itself. Any mathematical relationships arrived at by manipulating abstract statements may or may not convey something truthful about the thing being modelled. (For example, if 2 cups of water are added to 3 cups of water and the abstract mathematical operation 2+3 = 5 is used to calculate the total, the correct answer is 5 cups of water. However, if 2 cups of sugar are added to 3 cups of hot tea and the same operation is used, 5 is an incorrect answer.
Mathematical processes can lead to a kind of model of a thing, from which insights can be gained about the thing itself. Any mathematical relationships arrived at by manipulating abstract statements may or may not convey something truthful about the thing being modelled. (For example, if 2 cups of water are added to 3 cups of water and the abstract mathematical operation 2+3 = 5 is used to calculate the total, the correct answer is 5 cups of water. However, if 2 cups of sugar are added to 3 cups of hot tea and the same operation is used, 5 is an incorrect answer.
ChapterA: Working With Diagrams
Section: Chapter Questions
Problem 2QP
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Mathematical processes can lead to a kind of model of a thing, from which
insights can be gained about the thing itself. Any mathematical relationships
arrived at by manipulating abstract statements may or may not convey
something truthful about the thing being modelled.
(For example, if 2 cups of water are added to 3 cups of water and the
abstract mathematical operation 2+3 = 5 is used to calculate the total, the
correct answer is 5 cups of water. However, if 2 cups of sugar are added to 3
cups of hot tea and the same operation is used, 5 is an incorrect answer.)
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