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
Godel's unprovable statement - Numberfile
Reply to thread
Message
[QUOTE="PeroK, post: 6029638, member: 493650"] The idea is a version of Russell's paradox: [URL]https://en.wikipedia.org/wiki/Russell%27s_paradox[/URL] What Godel did was to construct a statement (by ingeniously getting number theory to talk about itself) that effectively said: "This statement cannot be proved from the given axioms." Now, if you prove that statement, then you have a contradiction. And, if you cannot prove it, then it is a[U] true statement that cannot be proved[/U]. This is the key point. The statement itself is true, in the sense that it cannot be false. But, this cannot be proved using the axioms. Hence, your axiomatic system cannot be used to prove all true statements. This leads to the concept of an undecidable proposition. [/QUOTE]
Insert quotes…
Post reply
Forums
Mathematics
Set Theory, Logic, Probability, Statistics
Godel's unprovable statement - Numberfile
Back
Top