26.9k views
2 votes
Insider the vector space ( mathbb{R} of sequences with an infinite tail of zeroes. In other words, given a quence ( in mathbb)one can find a number ( N ) such that al

User David EGP
by
8.1k points

1 Answer

4 votes

Final answer:

The question pertains to a vector space in Mathematics, specifically sequences with an infinite tail of zeroes within the space of real numbers.

Step-by-step explanation:

The student is asking about a concept in Mathematics, specifically about a vector space over the field of real numbers (denoted by \( \mathbb{R} \)). The vector space in question consists of all sequences that eventually become zero and remain zero thereafter (referred to as having an 'infinite tail of zeroes').

Formally, a sequence \( (a_n) \) belongs to this space if there exists a non-negative integer \( N \) such that for all \( n > N \), the sequence elements \( a_n = 0 \). This property ensures that beyond a certain point, the sequence contains only zeroes. Examples of sequences in this space include \( (1, 2, 0, 0, 0, \ldots) \) and \( (3, -1, 4, 0, 0, 0, \ldots) \), where after a finite number of terms, the sequence is entirely composed of zeroes.

User Sinaza
by
7.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.