What are the Implications of this thought I had?

[mr3000]

TL;DR

For any natural number n, there exists an infinite number of natural numbers higher than n, and a finite number of natural numbers smaller than n. Therefore, n is always infinitely closer to 0 than infinity

For any natural number n, there exists an infinite number of natural numbers higher than n, and a finite number of natural numbers smaller than n. Therefore, n is always infinitely closer to 0 than infinity

What does this mean?

 

[renormalize]

Therefore, n is always infinitely closer to 0 than infinity

Please define what it means to be "infinitely closer", as compared to just being "closer".

 

[mr3000]

Please define what it means to be "infinitely closer", as compared to just being "closer".

It means that there is an infinite distance between any natural number n and infinity, and a finite distance between n and zero.

 

[Petek]

As my advisor used to say, "All numbers are small, but most numbers are big."

 

[FactChecker]

TL;DR: For any natural number n, there exists an infinite number of natural numbers higher than n, and a finite number of natural numbers smaller than n. Therefore, n is always infinitely closer to 0 than infinity

For any natural number n, there exists an infinite number of natural numbers higher than n, and a finite number of natural numbers smaller than n. Therefore, n is always infinitely closer to 0 than infinity

Certainly, for any fixed number, n, and any multiplier, M, n is more than M times far away from infinity than it is from 0.

What does this mean?

If this is your thought, you might be better able to answer your question. Are you asking what it implies or what it literally means?
I expressed what I think it literally means. I don't think it implies anything profound.

 

[Matterwave]

Given $n\in\mathbb{N}$, the cardinality of the set of numbers $\{x\in \mathbb{N}|x\leq n\}$ is n. The cardinality of the set of numbers $\{x\in \mathbb{N}|x>n\}$ is countably infinite. However cardinality is a measure of the sizes of sets. It is not usually defined to mean distances. The "distance to infinity" of a natural number is not a commonly defined concept as far as I know. You could just say "it's infinite" but what is the utility of doing that?

 

[Dale]

TL;DR: For any natural number n, there exists an infinite number of natural numbers higher than n, and a finite number of natural numbers smaller than n. Therefore, n is always infinitely closer to 0 than infinity

infinite number of natural numbers higher than n, and a finite number of natural numbers smaller than n

Here you are talking about cardinality, the number of elements in a set.

TL;DR: For any natural number n, there exists an infinite number of natural numbers higher than n, and a finite number of natural numbers smaller than n. Therefore, n is always infinitely closer to 0 than infinity

Therefore, n is always infinitely closer to 0 than infinity

Here you are talking about distance, a different concept.

There are an infinite number of real numbers $0<x<1$, but any two integers $0 \le n \le 10$ are further apart even though there are fewer of them.

You really cannot exchange the concepts of distance and cardinality.

 

[martinbn]

TL;DR: For any natural number n, there exists an infinite number of natural numbers higher than n, and a finite number of natural numbers smaller than n. Therefore, n is always infinitely closer to 0 than infinity

For any natural number n, there exists an infinite number of natural numbers higher than n, and a finite number of natural numbers smaller than n. Therefore, n is always infinitely closer to 0 than infinity

What does this mean?

It means nothing special. You are stating something obvious.