User blog:VoidSansXD/Ordinal notation

Rules:

1.)  Δ1 = w

2.)  Δ2 = e0

3.)  Δ3 = z0

4.)  Δ4 = n0

5.)  Δn = the nth symbol

6.)  Δ(Δ1) = Δw

7.)  Δ(Δ2) = Δe0

8.)  Δ(Δ3) = Δz0

9.)  Δ(Δ4) = Δn0

10.)  Δ(Δ(1)) = Δ(Δw)

11.)  Δ(Δ(2)) = Δ(Δe0)

12.)  Δ(Δ(Δ(1))) = Δ(Δ(Δw))

13.)  Pattern repeats

14.)  ΔΔn = Δ(Δ(Δ(Δ(Δ(......Δ(Δ(Δ(1)))...))) with n triangles

15.)  There's always going to be an assumed one after the triangles

16.)  ΔΔw = Δ(Δ(Δ......Δ(Δ(1)))...))) with w Δ's.

17.)  ΔΔ(Δ1) = ΔΔw

18.)  ΔΔ(Δ2) = ΔΔe0

19.)  Pattern Repeats

20.)  ΔΔΔn = ΔΔ(ΔΔ(ΔΔ(ΔΔ.....ΔΔ(ΔΔ(ΔΔ(ΔΔ(ΔΔ1))))...))) with n ΔΔ's.

21.)  ΔΔΔΔn = ΔΔΔ(ΔΔΔ(ΔΔΔ......ΔΔΔ(ΔΔΔ1)))...)))) with n ΔΔΔ's.

22.)  Pattern repeats

23.)  Δ_1 = Δ1

24.)  Δ_2 = ΔΔ1

25.)  Δ_3 = ΔΔΔ1

26.)  Pattern repeats

27.)  ΔΔ_1,n = Δ_(Δ_(Δ_....Δ_(Δ_1))))....)))) with n Δ_'s.

28.)  ΔΔΔ_1,n = ΔΔ_(ΔΔ_(ΔΔ_....ΔΔ_(ΔΔ_1)))..))) with n ΔΔ_'s.

29.)  Pattern repeats.

30.)  Δ__1 = Δ_1,n.

31.)  Δ__2 = ΔΔ_1,n

32.)  Δ__3 = ΔΔΔ_1,n

33.)  Pattern repeats.

34.)  ΔΔ__1,n = Δ__(Δ__(Δ__(Δ__(....Δ__(Δ__1))))...)))))) with n Δ's.

35.)  Pattern repeats

36.)  Δ___1 = Δ__1,n

37.)  Δ___2 = ΔΔ__2,n

38.)  ΔΔ___1,n = Δ___(Δ___(Δ___(Δ___....Δ___(Δ___1)))...)))) with n Δ___'s.

39.)  Pattern repeats with 4 _'s, 5 _'s, etc.

40.)  FINAL RULE (unless I make an extended version :p);  yΔ--x--1,n = ΔΔΔΔ....ΔΔΔΔ____....___1,n with y triangles and x underscores.