Proving Denumerability of Positive Multiples of Three Greater Than 100

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Homework Help Overview

The discussion revolves around proving that the set of positive multiples of three greater than one hundred is denumerable. The original poster presents a function intended to demonstrate this property.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to establish a bijection between the natural numbers and the set S by defining a specific function. They seek validation of their approach and express uncertainty about their reasoning.

Discussion Status

Some participants provide reassurance regarding the original poster's method, indicating that it is correct. However, there is an underlying theme of uncertainty from the original poster about their understanding of the concepts involved.

Contextual Notes

The original poster mentions that this is their first experience with this level of mathematics, which may contribute to their uncertainty about the correctness of their approach.

eibon
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Homework Statement



Let S be the set of positive multiples of three which are greater than one hundred.
Show that S is denumerable.

Homework Equations


The Attempt at a Solution


let [tex]\phi[/tex]: [tex]N[/tex] [tex]\rightarrow[/tex] S
be given by [tex]\phi[/tex](n)= 99+3n is a bijection
thus it is denumerable

can someone tell me if that is right? if not can you tell me what i did wrong?
 
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Why would you think it's not right? It is.
 
well its the first time I am taking an math class like this and I am just not sure if I am doing things right
 
eibon said:
well its the first time I am taking an math class like this and I am just not sure if I am doing things right

Well, you are doing it right.
 
Thanks for the reassurance
 

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