There Is No Zero

Bruce Ediger
Bruce Ediger's web pages

This page contains a rant that I wrote to see if I could write like a mathematics crank. It appeared as a usenet article in September of 1998. It turns out that the someone already invented the numbering system I propose below. Robert Forslund wrote an article about it that appeared in a referreed journal. He calls the system below the "Alternate Numbering System". He uses A where I proposed using # (mockingly referring to it as "futplex", rather than one of #'s other names).

Forslund has thought a lot about zero and the way we write down positive integers.

Vicenzo Manca has written On the lexicographic representation of numbers, a summary of much of what is known about this kind of representation of numbers.

One interesting mathematical use of this Alternate Numbering System involves numbering strings in a particular alphabet. Suppose that our alphabet is {a, b, c, ..., z} (lower case English letters). All strings in the alphabet, including the empty string, can be uniquely enumerated by letting zero be the number of the empty string, and counting everying else in a base-26 variant of the system proposed below. This implies that the set of all strings over a given alphabet is countable, and if the length of the strings isn't constrained, the set of all strings over that alphabet is countably infinite.

String Number Decimal number
""
0
0
"a"
1
1
"b"
2
2
"c"
3
3
"z"
#
26
"aa"
11
27
"ab"
12
28
"ac"
13
29
"az"
1#
52
"za"
#1
677
"zz"
##
702
You get the picture.


Rant On

I will hereby prove that all of Modern Mathematics is based on a FALSE foundation: ZERO.

Q: Since ZERO is NOTHING, how can we have a SYMBOL to represent it?
A: We can't. NOTHING is NOTHING, the symbol we call zero ('0') is a FALSEHOOD!

Q: But HOW can we represent numbers without a ZERO!?!?
A: Like this! I'll use 'I' to represent a unit, which is the SMALLEST possible quantity. I'll use 'D' to represent ten units.

COUNT UNITS
1 I
2 II
3 III
4 IIII
5 IIIII
6 IIIIII
7 IIIIIII
8 IIIIIIII
9 IIIIIIIIII
#* D
11 DI
12 DII
13 DIII
14 DIIII
15 DIIIII
16 DIIIIII
17 DIIIIIII
18 DIIIIIIII
19 DIIIIIIIII
1#* DD
21 DDI

You get the picture. No symbol for NOTHING need exist, and in fact CAN exist. It stands to reason that you can't SYMBOLIZE NOTHING. With the introduction of '#'*, we can quit using zero for NOTHING or for anything. Now, a way exists to represent EVERY number without a symbol for NO NUMBER.

QED, Mathematics must be rebuilt upon this Firm, LOGICAL foundation.


* - Suggested pronunciation for the '#' sign: "futplex".

Example: "We humans all have futplex toes," Tom said tensely.
Example: "The act of killing one of every futplex prisoners is called 'decimating'," Tom concluded.


Rant Off

$Id: crank.rant.html,v 1.5 1999/06/07 04:17:34 bediger Exp bediger $

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