All Questions
6
questions
2
votes
0
answers
86
views
Is there a name for this set-theoretical definition of natural numbers, or has it been invented?
I'll call it the binary encoding with sets. I think it's nice and trivial, should have been discovered by many genius brains, but i can't find it by searching with efforts.
Prior arts are Zermelo's ...
- 109
2
votes
1
answer
186
views
Is the set of all linear orders on $\mathbb{N}$ linearly orderable?
In studying the issue of linear orders and well ordering in the context of ZF Set Theory (without the Axiom of Choice), I have recently been thinking about the following question:
Is the set of all ...
- 4,331
0
votes
1
answer
125
views
What is the cardinality of non-singleton subsets of $\mathbb{N}$?
I am studying a course on ZF Set Theory (without the Axiom of Choice) and am currently looking at the cardinalities of infinite sets. One question that I came across is the following:
Determine the ...
- 4,331
3
votes
1
answer
490
views
Is this exercise from Tao's Analysis 1 erroneous?
On page 68 of the fourth edition of Tao's Analysis 1, is Exercise $3.5.12$, the first part of which I believe is erroneous. The exercise is stated as follows:
(Note: $n++$ refers to the successor of $...
- 469
0
votes
3
answers
258
views
Can the natural numbers contain an element that is not representable by a number?
I read the following document: https://www.math.wustl.edu/~freiwald/310peanof.pdf . In this document, the author wants to formalize that natural numbers, that are informally thought of as a collection ...
- 389
3
votes
1
answer
364
views
Showing that the natural numbers are totally ordered with respect to set membership
Working with the usual set theoretic construction of the natural numbers, denoted $\omega$ for now.
I am trying to show that $\omega$ is totally ordered with respect to set membership, that is, $n<...
- 3,612