# Cantor Expressions

1. Oct 14, 2005

### raross

What is the cantor expansion of:

A. 2
B. 7
C. 19
D. 87
E. 1000
F. 1,000,000

The algorithm to solve these small problems is the most difficult for me.
The algorithm that I came up with states:
Asub(n) N! + Asub(n-1) (n-1)! +....+ Asub(2)2! + Asub(1)1!, where
Asub1 is an integer with 0 <= Asubi <= i for i = 1,2,....n,

I have tried to find other information on google, and have failed. It seems there is not much help with cantor expressions. So any help would be grateful!

2. Oct 14, 2005

### EnumaElish

Have you seen http://www.rose-hulman.edu/mathjournal/2004/vol5-n1/paper4/v5n1-4do.doc [Broken]?

This has an algorithm to convert a decimal number to Cantor.

Last edited by a moderator: May 2, 2017
3. Oct 14, 2005

### raross

So do these answers make sense or am I doing it wrong?

2 = 1*1! + 1
7 = 2*2! + 1*1! + 2
19 = 2*2! + 1*1! + 14
87 = 3*3! + 2*2! + 1*1! + 64

4. Oct 14, 2005

### raross

Im not sure how many digits you can put at the end, but it only makes sense I guess. Anyone help?

5. Oct 15, 2005

### raross

2 = 1*1! + 1
7 = 2*2! + 1*1! + 2
19 = 3*3! + 1
87 = 4*4! - 9