natural number

[ 2 r ]} when r is anodd natural number or m [member of] { 0, ...

First note using Lemmas 6 and 7 that for any multi-indices l, m, n and any natural number i we have

Following [13], recall that a sequence [([x.sub.n]).sub.n[member of]N] in E is called an e-uniform Cauchy sequence whenever, for every [epsilon] > 0, there exists a natural number N such that [absolute value of [x.sub.m] - [x.sub.n]] [less than or equal to] [epsilon]e holds for all m, n [greater than or equal to] N.

Although, the conjecture is not true for an integer r [greater than or equal to] 6 that is not a prime power, it is possible to prove a weak version of the topological Tverberg conjecture, more precisely, in this paper we show that if r is a natural number with prime factorization [mathematical expression not reproducible] then there is, for each j = 1,..., k, a set with r closed sides mutually disjoint of [[DELTA].sub.N] which can be divided into [mathematical expression not reproducible] subsets, each one having [[p.sub.j.sup.n].sup.j] elements, whose images have a common point.

SOME PEOPLE JUST MAKE GREAT NO 2S LOOK at every career, and you'll find natural number ones and natural number twos.

"She is a natural number 10, with a great pass and a real football brain, so she has the works," added her 45-year-old dad.

But there is no natural number two in the field, no similarly sized player who can be competitive on a national basis with the 34th Street Bunch.

Thus, wound care products will remain in demand, also due to the natural number of different injuries.

Define a natural number n to be thin if the standard prime decomposition for [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] has k = 1 for i = 1, 2, 3 ...

For the natural number n [greater than or equal to] 3,

By hypotheses (H3), we have, for any natural number h and i [member of] N,

For a given natural number, n, the sieve tests potential divisors up to [square root of n].

(iii) For each [??] > 0, there exist a natural number n and a real number [delta] > 0 such that for each integer p [greater than or equal to] n, each point x [member of] K and each mapping B [member of] A satisfying d(B, A) [less than or equal to] [delta], we have [parallel][B.sup.p](x)-[x.sub.A][parallel] [less than or equal to] [??].