Produce an explicit bijection between rationals and naturals
Oct 24, 2010 · From there, we can use any of the bijections $\mathbb N\to\mathbb Z$ to get our bijection between $\mathbb N$ and $\mathbb Q$. (We'll need a specific such bijection below, …
Is there a natural bijection from $\mathbb {N}$ to $\mathbb {Q…
Mar 22, 2015 · If one is willing to consider the prime factorisation coming from the fundamental theorem of arithmetic as "natural", then the problem reduces to finding a "natural" bijection …
Bijection - Wikipedia
The elementary operation of counting establishes a bijection from some finite set to the first natural numbers (1, 2, 3, ...), up to the number of elements in the counted set. It results that …
A Bijection from N to Q: Explicit Formula for Rational Numbers
Jun 29, 2007 · I am bored and feel like doing something useless today so I'm going to try to give an explicit formula that maps N to Q that is a one-to-one correspondence...
We will produce a bijection between plane trees and the parentheses expressions considered in the previous problem. We first describe an algorithm to turn a plane tree into a parentheses …
elementary set theory - Bijection between $N$ and $Q ...
Nov 12, 2017 · Further you may define a relation between negative rationals $Q^-$ and natural numbers in a similar fashion.
How nice can a bijection between $\mathbb {N}$ and $\mathbb ...
Jan 5, 2025 · This question is similar to: Is there a natural bijection from $\mathbb {N}$ to $\mathbb {Q}$?. If you believe it’s different, please edit the question, make it clear how it’s …