8.2: Incompleteness of axiomatic systems
- Page ID
- 83440
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It turns out that if we want to create an axiomatic system on which to base mathematics, we will always run into problems, and some things will remain out of our reach.
In any axiomatic system that is sufficiently complex for it to be possible to prove certain basic facts about the nonnegative whole numbers, it is possible to devise a statement that is true but unprovable.
May you never attempt to prove a statement that is true but unprovable!