Can a Sequence Visit 0, 1, and 5 Infinitely Often?

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Homework Help Overview

The discussion revolves around constructing a sequence that visits the numbers 0, 1, and 5 infinitely often. The context is within the study of sequences in mathematics, particularly focusing on the properties of infinite visits to specific values.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants explore various sequence constructions, questioning the validity of specific examples and whether they meet the criteria of visiting the specified numbers infinitely often.

Discussion Status

The discussion includes attempts to clarify misunderstandings about sequence definitions and properties. Some participants have offered potential sequence ideas while others express uncertainty about their effectiveness.

Contextual Notes

There is a mention of confusion regarding the definitions and properties of sequences, as well as the need for clarity on what it means to visit numbers infinitely often. Some participants are considering broader mathematical concepts that may relate to the problem.

adrivit
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Construct a sequence that visits the numbers 0,1,5 infinitely often.
A sequence Sn visits a number A when for infinitely many n in N, Sn = A. Example: The sequence (-1)^n visits -1 and 1 infinitely.
 
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What's wrong with a3n= 0, a3n+1= 1, a3n+2= 5 for all n?
 
But, the function doesn't visit 0,1,5 infinitely many times here does it?
 
I'm sorry, I misunderstood. Thanks for the solution!
 
How about the sequence which visits all N infinitely?
 
Do you have any ideas? There is one that is fairly similar to the one that visits 0,1 and 5 infinitely often
 
I was wondering whether N mod N would do the trick. Or maybe considering the field R^inf and the sub field N inside that. But I am not sure of either.
 

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