All Questions
4
questions
1
vote
2
answers
71
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How is ($\mathbb{Z}\setminus\mathbb{Q}$) a subset of $\mathbb{N}$?
I do not understand why the set ($\mathbb{Z}\setminus\mathbb{Q}$) is a subset of $\mathbb{N}$. $\mathbb{Q}$ extends the $\mathbb{Z}$ by adding fractions. So there cannot be an element in $\mathbb{Z}$ ...
- 21
0
votes
2
answers
494
views
Set of natural and rational numbers
Just a quick question: Is it correct to say that the set of rational numbers cannot be a subset of the set of natural numbers? Certainly, we know these two sets have the same cardinality and there ...
- 71
0
votes
0
answers
64
views
Limiting set of scaled natural numbers $\mathbb{N}$
This may be a non-standard question, and possibly irrelevant to the participants. Nevertheless, after reading the first chapter of Terence Tao's book on measure theory, I ended up thinking about what ...
- 121
127
votes
9
answers
76k
views
Produce an explicit bijection between rationals and naturals
I remember my professor in college challenging me with this question, which I failed to answer satisfactorily: I know there exists a bijection between the rational numbers and the natural numbers, but ...
- 4,251