# Vlorbik's Diner

## exercises at random

Posted by vlorbik on December 3, 2009

D1: 0
0:=[]

D2: ^
s^:=su[s]

D3: 1
1 := 0^

T: 1=[0].
P:
1=
0^=
[]^=
[]u[[]]=
[[]]=
[0]
.

D4: 2
2:=1^

T: 2=[0,1].
P:
2=
1^=
[0]^=
[0]u[[0]]=
[0,[0]]=
[0,1]
.

Exercise.
i. Define the symbol “3”
appropriately and show
that 3=[0,1,2].
ii. Do it again another way.
iii. Close the book
and check that
3=[[],[[]],[[],[[]]]].

hint: lay out your
work on the page
systematically to
keep track of parens
and commas better.
(every keystroke is
life or death.)
it’s actually easier
you can cut and paste
and wipe out spaces
& whatnot. yep.
extra credit.
find the bug in the code.

4=[[],[[]],[[],[[]]],[[],[[],[[],[[]]]]]

1. ### vlorbiksaid

http://bryangoodrich.wordpress.com/2009/03/21/how-to-create-everything-from-nothing/

2. ### vlorbiksaid

the link in the previous comment has rotted away.
as i recall, it was some darn good exposition on
the “construct the natural numbers using elementary
set theory” thing that my post deals with here
(as sort of an exercise in minimalism). hmm.

as usual, w’edia is pretty good.

(but “counting numbers” for {0, 1, 2, …}?
never in any other source i can recall.)

3. ### cut & paste | the livingston reviewsaid

[…] exercises at random S^ := S cup […]

4. ### Vlorbik On Math Ed | the livingston reviewsaid

[…] 12/03/09 exercises at random S^ := S cup […]