MathDB

Given is a sequence of real numbers

\{a_n\}^{\infty}_{n=1}

such that

a_n \ne a_m

for

n\ne m,

given is a natural number

k

. Construct a simple representation

P

of the set

1,2,...,20k

into the set of natural numbers to apply

a_{p(1)}<a_{p(2)}<...<a_{p(10)}

a_{p(10)}>a_{p(11)}>...>a_{p(20)}

a_{p(20)}<a_{p(21)}<...<a_{p(30)}

...

a_{p(20k-10)}>a_{p(20k-9)}>...>a_{p(20k)}

a_{p(10)}>a_{p(30)}>...>a_{p((20k-10))}

a_{p(1)}<a_{p(20)}<...<a_{p(20k)},

[hide=original wording of first sentence]Daná je postupnos’ reálných čísel {a_} také že an \ne a_m ctm pre n\ne m, dané je prirodzené číslo k. Zostrojte prosté zobrazenie P množiny 1,2,...,20k do -množiny prirodzených . čísel , aby platilo

Problem Statement