To wit, when we seek to subject them to numeration ... we find that they flee away perpetually, so that not one of them can be apprehended precisely in itself. . . . Now that cannot be called a true number which is of such a nature that it lacks precision.... The Teaching of Algebra (including Trigonometry) - 412. lappuseautors: Sir Thomas Percy Nunn - 1914 - 616 lapasPilnskats - Par šo grāmatu
| Sir Thomas Percy Nunn, Thomas Percy Nunn - 1914 - 616 lapas
...only if neither the lengths of the lines nor the areas of the squares upon them are commensurable. 2 **The table of binomial coefficients given on p. 213...is easily seen that each irrational falls between** 0 ifi FIG. 92. two consecutive integers. Also they are not fractions with definite numerators and denominators,... | |
| Sir Thomas Percy Nunn - 1919 - 616 lapas
...commensurable. 2 The table of binomial coefficients given on p. 213 appears in Book I of this work (folio 45). **one hand, argues Stifel, " since, in proving geometrical...easily seen that each irrational falls between APBX** o ~ ; " ? l FIG. 92. two consecutive integers. Also they are not fractions with definite numerators... | |
| Morris Kline - 1982 - 366 lapas
...irrational numbers are numbers at all. To wit, when we seek to subject them to numeration [decimal form] ... **we find that they flee away perpetually so that not...number, but lies hidden in a kind of cloud of infinity.** Then Stifel added that real numbers are either whole numbers or fractions, and, obviously, irrationals... | |
| Morris Kline - 1990 - 428 lapas
...are numbers at all. To wit, when we seek to subject them to numeration [decimal representation] ... **we find that they flee away perpetually, so that not...number, but lies hidden in a kind of cloud of infinity,** He then argues that real numbers are either whole numbers or fractions; obviously irrationals are neither,... | |
| Shaughan LAVINE - 1994 - 372 lapas
...irrational numbers are numbers at all. To wit, when we seek [to give them a decimal representation] ... **we find that they flee away perpetually, so that not...number, but lies hidden in a kind of cloud of infinity.** [KH72, p. 251] As we shall see, Stifel's remarks were prescient: the basis of the irrational numbers... | |
| Art Johnson - 1999 - 179 lapas
...example, AAAA to represent AA. He did not, however, have a grasp of irrational numbers, writing that **"an irrational number is not a true number, but lies hidden in** some sort of cloud of infinity." Although Stifel solved quadratic equations with negative roots, he... | |
| Gerard G. Emch, Chuang Liu - 2002 - 703 lapas
...[2,2,2,2,2,2,2,2, ...] e =2+ [1,2,1, 1,4,1, 1,6,...] \ (5.4.7) TT =3+ [7,15,1,292,1,1,1,2, . . .] J **an irrational number is not a true number but lies hidden in a kind of cloud of infinity.** |Stifel, 1544] Euler [1744a] proved in 1737/44 that the simple continued fraction expansion of every... | |
| David Foster Wallace - 2003 - 319 lapas
...irrational numbers are numbers at all. To wit, when we seek to subject them to [decimal representation], **we find that they flee away perpetually, so that not...number, but lies hidden in a kind of cloud of infinity.** §2d. "UNAVOIDABLE BUT ULTIMATELY IYI-GRADE INTERPOLATION Skip the following few pages if you like,... | |
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