Minimalist ordinal notation (MON) is an ordinal notation using only two symbols.
- 0 = \(0\)
- wαβ = \(\omega^\alpha+\beta\) where α β are strings representing the ordinals \(\alpha\) and \(\beta\)
Comparison to traditional notation[]
- 0 = \(0\)
- w00 = \(1\)
- w0w00 = \(2\)
- w0w0w00 = \(3\)
- w0w0w0w00 = \(4\)
- w0w0w0w0w00 = \(5\)
- ww000 = \(\omega\)
- ww00w00 = \(\omega+1\)
- ww00w0w00 = \(\omega+2\)
- ww00w0w0w00 = \(\omega+3\)
- ww00ww000 = \(\omega\cdot2\)
- ww00ww00w00 = \(\omega\cdot2+1\)
- ww00ww00ww000 = \(\omega\cdot3\)
- ww0w000 = \(\omega^2\)
- ww0w00w00 = \(\omega^2+1\)
- ww0w00w0w00 = \(\omega^2+2\)
- ww0w00ww000 = \(\omega^2+\omega\)
- ww0w00ww00w00 = \(\omega^2+\omega+1\)
- ww0w00ww00ww000 = \(\omega^2+\omega\cdot2\)
- ww0w00ww00ww00w00 = \(\omega^2+\omega\cdot2+1\)
- ww0w00ww00ww000 = \(\omega^2+\omega\cdot3\)
- ww0w00ww0w000 = \(\omega^2\cdot2\)
- ww0w00ww0w00w00 = \(\omega^2\cdot2+1\)
- ww0w00ww0w00ww000 = \(\omega^2\cdot2+\omega\)
- ww0w00ww0w00ww00ww000 = \(\omega^2\cdot2+\omega\cdot2\)
- ww0w00ww0w00ww0w000 = \(\omega^2\cdot3\)
- ww0w0w000 = \(\omega^3\)
- ww0w0w00ww0w0w000 = \(\omega^3\cdot2\)
- ww0w0w0w000 = \(\omega^4\)
- www0000 = \(\omega^\omega\)
- www000w00 = \(\omega^\omega+1\)
- www000w0w00 = \(\omega^\omega+2\)
- www000ww000 = \(\omega^\omega+\omega\)
- www000ww0w000 = \(\omega^\omega+\omega^2\)
- www000www0000 = \(\omega^\omega\cdot2\)
- www00w000 = \(\omega^{\omega+1}\)
- www00w0w000 = \(\omega^{\omega+2}\)
- www00ww0000 = \(\omega^{\omega\cdot2}\)
- www0w0000 = \(\omega^{\omega^2}\)
- wwww00000 = \(\omega^{\omega^\omega}\)
- wwww0w00000 = \(\omega^{\omega^{\omega^2}}\)
- wwwww000000 = \(\omega^{\omega^{\omega^\omega}}\)
- wwwwww0000000 = \(\omega\uparrow\uparrow5\)
- wwwwwww00000000 = \(\omega\uparrow\uparrow6\)
The limit of the system is \(\varepsilon_0\).