The Nature And Utility of Mathematics, With the Best Methods of Instruction Explained And Illustrated

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bers. Hence, A NUMBER is a unit or a collection of units.
IDEAS OF NUMBERS GENERALIZED.
Ideas of § 114. If wc begin with the idea of the num- generaiized. ^cr onc, and then add it to one, making two ; and then add it to two, making three ; and then to thi'ee, making four ; and then to four, making How formed, fivc, and SO On ; it is plain that we shall form a series of numbers, each of which will be greater Hnity the bv onc than that which precedes it. Now, one or unity, is the basis of this se
...ries of numbers.
Three ways of expressing and each number may be expressed in three them.
ways : 1st way. 1st. By the words one, two, three, &c., of our common language ; 2d way. 2d. By the Romaii characters ; and, 3d way. 3d. By figures.
CHAP. II.] .ARITHMETIC UNITY. 12,1 notions are complex.
§ 115. Since all numbers, whether integral or AUanmbers ^ . , P 111 come from rractional, must come irom, and hence be con- ^ne: nected with, the unit one, it follows that there is but one purely elementary idea in the science of numbers.


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