Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
General Math
Calculus
Differential Equations
Topology and Analysis
Linear and Abstract Algebra
Differential Geometry
Set Theory, Logic, Probability, Statistics
MATLAB, Maple, Mathematica, LaTeX
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
General Math
Calculus
Differential Equations
Topology and Analysis
Linear and Abstract Algebra
Differential Geometry
Set Theory, Logic, Probability, Statistics
MATLAB, Maple, Mathematica, LaTeX
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Mathematics
Set Theory, Logic, Probability, Statistics
ZFC .... Axioms of Foundation .... and Infinity ....
Reply to thread
Message
[QUOTE="Math Amateur, post: 5809472, member: 203675"] I am reading D. J. H. Garling's book: "A Course in Mathematical Analysis: Volume 1: Foundations and Elementary Real Analysis" ... ... I am at present focused on Part 1: Prologue: The Foundations of Analysis ... Chapter 1: The Axioms of Set Theory ... I need help with an aspect of the proof of Proposition 1.7.5 ... Proposition 1.7.5 reads as follows:[ATTACH=full]207761[/ATTACH] In the above proof we read the following: "By the foundation axiom, there exists ##n \in \mathbb{Z}^+## such that no member of ##f(n)## is in ##f( \mathbb{Z}^+ )##. ... ... " Can someone please explain how/why the foundation axiom implies that there exists ##n \in \mathbb{Z}^+## such that no member of ##f(n)## is in ##f( \mathbb{Z}^+ )##. ... ... ? PeterNOTE: To enable readers to follow the above post I am providing Garling's text on the foundation axiom and the axiom of infinity ... ...[ATTACH=full]207762[/ATTACH] [ATTACH=full]207763[/ATTACH] [/QUOTE]
Insert quotes…
Post reply
Forums
Mathematics
Set Theory, Logic, Probability, Statistics
ZFC .... Axioms of Foundation .... and Infinity ....
Back
Top