144 Normat 52:3, 144 (2004)

Summary in English

Vagn Lundsgaard Hansen, Around

infinity (Danish.) The author discusses

the notion of infinity in the histori-

cal and philosophical context in which

it developed from Greek roots, such

as Zeno’s Paradoxes, to its mathemat-

leads to a proof of uncountability differ-

ent f rom the usual diagonal arguments.

The article ends with a little cardinal

arithmetic illustrated by Hilbert’s Ho-

tel.

Bengt Ulin, Even this many exam-

ples do not suffice. . . (Swedish.) The

author discusses a divisibility question

that links the binary and decimal rep-

resentations of integers. A binary string

a decimal expansion with all digits equal

to 0 or 1, and suppose the integer is di-

visible by eleven. Will the integer ob-

tained by reading the same decimal ex-

pansion in the binary system be divisi-

ble by three? The integer 1111 = 101·11

is divisible by eleven, and the same

string of digits represents the integer 15

in the binary system. And 15 is divisible

by three. Trying other small and not so

small examples, the rule always holds.

But ultimately, very ultimately, it fails!

it fails for 101010101010101010101.

Maria Deijfen, Epidemics on social

graphs (Swedish.) In most mathemati-

cal models for the spread of epidemics,

the population in which the epidemic

takes place is assumed to be homoge-

neously mixing, that is, no s ocial struc-

ture is assumed to exist in the popula-

tion. In this work it is d esc ribed how

this very unrealistic assumption can be

is one of the simplest stochastic mod-

a social network. Also, the effects on the

spread of the epidemic are quantified in

that asymptotic formulas for epidemi-

ological quantities like the basic repro-

epidemic are derive d.