## The new encyclopaedia Britannica: in 32 vol. Macropaedia, Accounting - Architecture, Volume 13 |

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Page 282

The 20th, predicted by Rudvalis, was constructed by Conway and Wales (see

233). (Ma.H.)

elements that are commonly called numbers, in which the four familiar operations

...

The 20th, predicted by Rudvalis, was constructed by Conway and Wales (see

233). (Ma.H.)

**Fields**Broadly speaking, a**field**is an algebraic system consisting ofelements that are commonly called numbers, in which the four familiar operations

...

Page 289

It is then straightforward to show that the above construction gives a non-

Archimedean ordered

series — i.e., extended formal power series (288) with r > 0 — is a subring, hence

a ...

It is then straightforward to show that the above construction gives a non-

Archimedean ordered

**field**. In this ordered**field**, the set of all ordinary powerseries — i.e., extended formal power series (288) with r > 0 — is a subring, hence

a ...

Page 290

strengthen to an inequality involving the maximum of two p-adic valuations rather

than the sum. There are many other important generalizations of the absolute

value concepts to systems other than

...

strengthen to an inequality involving the maximum of two p-adic valuations rather

than the sum. There are many other important generalizations of the absolute

value concepts to systems other than

**fields**: the absolute value (x2 + y2 + z2 + t2)...

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