From: utzoo!decvax!harpo!npoiv!alice!physics!gill
Newsgroups: net.jokes,net.math
Title: modulus moderation
Article-I.D.: physics.110
Posted: Wed Jul 28 23:31:35 1982
Received: Thu Jul 29 05:09:18 1982

I just read Berry's item saying the the mod joke was wrong but that
60 mod 20 = 3, not 30. I promised myself never to write this phrase again,
but I can't help it.

	* S I G H *

	As far as I know, there are two general meanings to the word
"modulus." One is used when talking about groups, the other when doing
division in computers (i.e. as an operator) or (gasp!) by hand.

	In the first context, we can create a modulus number system
with n elements labeled 0 through n-1 with bars on top to signify
that each "number" stands for a partition of the integers (i.e. an
equivalence class). Thus, the integers 0, 20, 40, 60, etc ... would
all be equivalent to 0 (bar) mod 20.

	In the computer or division context (i.e. the C "%" operator),
the idea is "remainder when dividing." For example, 13 mod 10 = 3 and
-13 mod 10 = -3 (it would be equivalent to +7 in real mathematics). To
find out what "number" an integer is really equivalent to in C,
you must say n % MOD + (n < 0 ? MOD : 0) [assuming % costs more
to do than +] or, if you know n goes no lower than 1 - MOD, (n + MOD) % MOD
will do. If MOD is a power of two, you can cheat by using n & (MOD - 1).

	No matter what method is used, 60 mod 20 is (or is equivalent)
to ZERO (or 0 bar). NOT 30. NOT 3.

	Perhaps as someone else pointed out if 60 were taken in base ten
then 30 would be the same number in base 20 if lefthand juxtaposition meant
increasing powers of 20. Sounds far fetched to me, but that's probably
what was indended.

	Anyway, 3 is nothing more than the floor of dividing 60 by
20. So what?

	Well, at least the original joke was better than the repulsive
one about M.I.T. "girls" (I prefer to call them women). Perhaps if
it had said something about a kernal named bertie and his girlfriend
named gertie, and how mod 20 there ages were same, it would have worked.

	Gill Pratt

	...alice!gill OR gill@mc

p.s. This points something else out. How about some debate on the
bookeeping of followup articles? Perhaps there should be some sort of
indication of whether other people have responded to a particular
article when you first encounter it. This will at least save some
face and also (I believe) a lot of traffic from repetitive answers.