We already did the PeanoAxioms
Recursive definition of +, *, <.
- Axioms for +, *
- ∑i up to n = n(n+1)/2
If x ≥ y, then ax ≥ ay—proven formally for x,y,a ∈ ℕ using the PeanoAxioms.
n2 < 2n for sufficiently large n
[FrontPage] [TitleIndex] [WordIndex]
|
|
[FrontPage] [TitleIndex] [WordIndex] |
Note: You are looking at a static copy of the former PineWiki site, used for class notes by James Aspnes from 2003 to 2012. Many mathematical formulas are broken, and there are likely to be other bugs as well. These will most likely not be fixed. You may be able to find more up-to-date versions of some of these notes at http://www.cs.yale.edu/homes/aspnes/#classes.
We already did the PeanoAxioms
Recursive definition of +, *, <.
If x ≥ y, then ax ≥ ay—proven formally for x,y,a ∈ ℕ using the PeanoAxioms.
n2 < 2n for sufficiently large n