 # Speaking of counting methods ...

That counting method you sometimes see:

A = 1
B = 2

Z = 26
AA = 27
AB = 28

etc. Is there a formal name for this style of sequencing other than something like “alphabetic numbering” which I might make up off the top of my head?

Base 26?

Not base 26. That would be:

0=0
1=1
2=2

10=A
11=B

24=O
25=P
26=10 (or 1,0 to distinguish it from “ten”)

Therefore the base ten representation of AA in base 26 would be 26*10+10=270, not 27

My best guess for the method given in the OP would be some variation on “alpha-numeric” sequencing, or something like that.

Natural Numbers are 1, 2, 3, 4 … (as contrasted with Integers, which include zero).

Even so, in the naturals, base 26, 1!=A. Even without zero, you still start with 1=1. And even without the number zero, the digit 0 still exists, in either base.

As an example, the number ten, base ten, is represented by “10” meaning “one ten, zero ones” (or better yet, “one ten-to-the first, zero ten-to-the-zeros”). Similarly, twenty-six, base twenty-six, is “1,0” meaning “one twenty-six, zero ‘ones’” (or “one twenty-six-to-the-first, zero twenty-six-to-the-zeros”).

Ahem…that went through a bit too soon by mistake…

As I was going to say, the different bases we are familiar with all share that same method of assigning symbols to the number. With the method given in the OP, that pattern is broken.

“base” is misleading. There’s no zero placeholder, so even if you bias it to zero:

A = 0
B = 1

Z = 25
AA = 26
AB = 27

You will note that the “number” can not be interpreted as a sum of multiples of powers of 26. The logic for producing the sequence, biased to zero, is something like this, in fact:

``````

private static void alphaseq0(int n, StringBuffer buf) {
if (n >= ALPHABET_LENGTH) {
alphaseq0(n/ALPHABET_LENGTH - 1,buf);
n = n % ALPHABET_LENGTH;
}
buf.append(ALPHABET.charAt(n));
}

``````

I’m not so interested in making up a plausible name, as finding out if somebody in the publishing industry or some such place has actually given it one.

Of course, the symbols associated with each number are completely arbitrary, so that doesn’t eliminate this as a “natural base” 26. And some characterizations of the naturals have no 0.

Oh no. Modulo math all over again.

Why not call it “The Yabob System”? If it doesn’t have a name, perhaps you can achieve immortality through the back door, so to speak.

Yabob

Have you seen this anywhere? Labeling lists and such uses A, B, C sometimes - does anone know if this ever goes to AB? (Come on, Publishers)

The zero-biased one looks like base-26 to me. (But not the usual symbols for it - something like base-26, starting at ‘a’ or starting at ‘b’ or based at ‘a’ or something) A would be the zero placeholder. Don’t know about the original system, though.

The identification of letters with numbers is part of numerology. Uusally, however, this just goes up to Zed.

A = 1, B = 2, C = 3, … Z = 26 is one approach. But you wouldn’t take AA = 27, AB =28… You’d just add. If you had a name like the group ABBA, you’d assign 1 + 2 + 2 + 1 = 6 as the numerological value.

A = 1, B = 2, … , J = 10, K = 20, L = 30, … , S = 100, T = 200, … Z = 800 is the more common approach. Gets more numbers involved.

The one biased to 0 is NOT base 26. if A=0, … Z=25, 26 is represented by “BA”, not “AA”. Like I said, there is no zero placeholder.

I would not call this base anything, biased either way, since you cannot interpret the represenation as a sum of the digits times powers of the base. Turn that code snippet I gave into a recursion formula if you would like a mathematical expression for it. The “-1” is crucial. You can bias it to 1 instead of 0, also - you’ll just have a few more “n-1” ’ s floating around in there.

Yes, I have seen this. In fact, there’s an example right in front of you right now. This is how both IE and Netscape treat <OL Type=A> lists. The next item after item “Z” is “AA”, the next “AB”, and so on. Desktop publishing programs which autonumber things often do it this way, to. nroff worked this way.

Documentation of such systems tends to skirt the issue, and avoid calling it anything beyond something like a “numbering style”, showing you by example what “style” A means. Usually not even documenting what happens after the Z’th item.

BTW, Microsoft Word does NOT do this. Autonumbered items in Word work like:

1 - A
2 - B

26 - Z
27 - AA
28 - BB
29 - CC

While we’re at it, is there a name for THAT system?