From: tanmoy@qcd.lanl.gov (Tanmoy Bhattacharya)
Subject: Re: Teaching sorts [was Re: What's the best language to start with?]
Date: 1996/08/21
Date: 1996-08-21T00:00:00+00:00 [thread overview]
Message-ID: <TANMOY.96Aug21164211@qcd.lanl.gov> (raw)
In-Reply-To: 01bb8f1b$ce59c820$32ee6fce@timhome2
In article <4vfk6b$i6h@krusty.irvine.com>
adam@irvine.com (Adam Beneschan) writes:
<snip>
AB: >No, but a complex Big-Oh function has *exactly* the same meaning as a
AB: >simpler one in most cases. Calling something a O(f(n)) function means
AB: >saying that (This may not be the technical definition: but this
AB: >expresses the meaning commonly used):
AB: >
AB: > 1) there exists k and N depending on k such that for all n > N, the
AB: > function in question is bounded in absolute value by by k |f(n)|.
AB: > 2) The minimum such k is non-zero. (This is to prevent a O(n)
AB: > function also being classified as a a O(nlogn) for example).
AB:
AB: I've never seen a definition of O(f(n)) that includes anything like
AB: (2). In the mathematical definitions I've seen, O(f(n)) provides only
AB: an upper bound on the value expressed by O-notation, not a lower
AB: bound. Under these definitions, it is perfectly correct (although not
AB: too useful) to say that a linear algorithm is O(n**2) or O(n**3).
Correct. Number (2) actually exists only to get it closer to common
usage without giving up the asymptotic nature of the definition.
AB:
AB: Perhaps someone else can provide a different definition? Tanmoy's
AB: statement as expressed above isn't precise enough to be a mathematical
AB: definition. Perhaps it means that there are two constants, kl and ku,
The (1) above is obviously rigorous.
The (2) above is completely rigorous statement expressing common
usage. The `minimum such k' refers to the minima of the set of allowed
k's (i.e. values of k for which an N exists): the minima may not
actually belong to the set.
AB: such that the value represented by O(f(n)) is between kl |f(n)| and ku
AB: |f(n)| for all n > N. This still may not be enough for people who
No. That does not capture the common meaning: if an algorithm is
trivial for odd N, but goes as N^2 for even N, it is still called
O(N^2). But, naturally, you can't find kl in this case.
AB: want O(f(n)) to give an approximation of proportional running time, so
AB: those people may want to add the restriction that kl/ku >= 0.95 or
AB: something to keep the running time from varying too much. And Tim
AB: wants a notation that puts bounds on the running time for *all* n, not
AB: just "large enough" n.
Yes if you want O() to be an approximation, you may want to use your
kl/ku solution.
AB:
AB: The more I follow this thread, the more I'm convinced that our use of
AB: O-notation is an abuse; we've twisted the original mathematical
AB: purpose of the notation beyond recognition. The first place I saw
AB: this notation used was in Knuth's _Art of Computer Programming_, and
AB: he only used it to express part of a formula that approaches zero as n
AB: gets large. For example:
AB:
AB: P(n) = sqrt(pi*n/2) - 2/3 + (11/24)*sqrt(pi/(2*n)) + 4/(135*n)
AB: - (71/1152)*sqrt(pi/(2*n**3)) + O(n**-2)
AB:
AB: Here, O(n**-2) refers to terms in the sum that eventually go to zero
AB: as n gets large. From what I could find, Knuth *never* uses it to
AB: describe the running time of an algorithm.
AB:
AB: Following this viewpoint, when we computer scientists speak of an
AB: algorithm's running time as O(n**2), mathematicians might say
AB:
AB: Running time = K * n**2 * (1 + O(1/n))
AB:
AB: for some constant K. The point here is that the proportional
AB: difference between the running time and (K * n**2) tends to disappear
AB: as n gets large (hence the O(1/n) term).
AB:
And as you can trivially show, the K in the above formula is the
minima of the set of k's that I was talking about. The two points of
view are identical. Except, when I (or almost anyone) calls something
O(N^2), the correction term need not be O(N): it may as well be
O(NlogN).
AB: In contrast to what I believe was the original purpose of O-notation,
AB: computer scientists are using the notation as a shorthand for
AB: "approximately proportional to." The original mathematical
No. It is used mainly in the theory of algorithmic complexity. Its use
as an approximation is only a loose usage: which is often, but not
always, correct.
AB: definition, which suited the purpose of expressing a quantity that
AB: tended toward zero, doesn't suit our purposes of classifying
The O notation is used for both small and large quantities. Its
original definition was that f(x) and g(x) were the same `order' if
lim f(x)/g(x) was neither 0 nor infinite as x went to something. This
definition can be easily modified if the limit does not exist, and I
think my definition is identical to that variation as long as we talk
about O(f) only for functions f that are monotonic for sufficiently
large N.
<snip>
AB: P.S. My theories about how mathematicians view and use O-notation may
AB: be incorrect. I might ask sci.math to enlighten me here. --ajb
Yes, the topic has gone far beyond the purview of most of the groups:
let us take this discussion elsewhere.
Cheers
Tanmoy
--
tanmoy@qcd.lanl.gov(128.165.23.46) DECNET: BETA::"tanmoy@lanl.gov"(1.218=1242)
Tanmoy Bhattacharya O:T-8(MS B285)LANL,NM87545 H:#9,3000,Trinity Drive,NM87544
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next prev parent reply other threads:[~1996-08-21 0:00 UTC|newest]
Thread overview: 688+ messages / expand[flat|nested] mbox.gz Atom feed top
[not found] <sperlman-0507961717550001@p121.ezo.net>
[not found] ` <4rs76l$aqd@ccshst05.uoguelph.ca>
1996-07-15 0:00 ` Should I learn C or Pascal? Ralph Silverman
1996-07-15 0:00 ` Steve Sobol
1996-07-16 0:00 ` Lee Crites
1996-07-17 0:00 ` David Verschoore
1996-07-17 0:00 ` Anthony Kanner
1996-07-17 0:00 ` Mark McKinney
1996-07-19 0:00 ` Philip Brashear
1996-07-23 0:00 ` John A Hughes
1996-07-26 0:00 ` Randy Kaelber
1996-07-29 0:00 ` Ralph Silverman
1996-08-06 0:00 ` StHeller
1996-07-20 0:00 ` TRAN PHAN ANH
1996-07-20 0:00 ` Mark Eissler
1996-07-25 0:00 ` Erik Seaberg
1996-07-26 0:00 ` What's the best language to start with? [was: Re: Should I learn C or Pascal?] Tim Behrendsen
1996-07-27 0:00 ` Rick Elbers
1996-07-28 0:00 ` Mark Eissler
1996-07-28 0:00 ` J. Christian Blanchette
1996-07-28 0:00 ` Robert Dewar
1996-07-29 0:00 ` Tim Behrendsen
1996-07-30 0:00 ` Arra Avakian
1996-07-31 0:00 ` Stephen M O'Shaughnessy
1996-07-31 0:00 ` James Youngman
1996-08-02 0:00 ` Tim Behrendsen
1996-08-05 0:00 ` Henrik Wetterstrom
1996-08-05 0:00 ` Fergus Henderson
1996-08-06 0:00 ` Tim Behrendsen
1996-08-06 0:00 ` Dan Pop
1996-08-06 0:00 ` Tim Behrendsen
1996-08-06 0:00 ` Peter Seebach
1996-08-07 0:00 ` Tim Behrendsen
1996-08-07 0:00 ` James A. Squire
1996-08-07 0:00 ` Peter Seebach
1996-08-08 0:00 ` Tim Behrendsen
1996-08-08 0:00 ` Peter Seebach
1996-08-08 0:00 ` David Weller
1996-08-09 0:00 ` Bob Gilbert
1996-08-10 0:00 ` Tim Behrendsen
1996-08-11 0:00 ` Peter Seebach
1996-08-11 0:00 ` Tim Behrendsen
1996-08-12 0:00 ` Alf P. Steinbach
1996-08-12 0:00 ` Tim Behrendsen
1996-08-13 0:00 ` Szu-Wen Huang
1996-08-11 0:00 ` Craig Franck
1996-08-11 0:00 ` Tim Behrendsen
1996-08-07 0:00 ` Mark Eissler
[not found] ` <01bb83cc$fb <tequila-0708960947140001@tequila.interlog.com>
1996-08-07 0:00 ` Peter Seebach
1996-08-06 0:00 ` Szu-Wen Huang
1996-08-06 0:00 ` Tim Behrendsen
1996-08-06 0:00 ` Peter Seebach
1996-08-07 0:00 ` Tim Behrendsen
1996-08-07 0:00 ` Dan Pop
1996-08-08 0:00 ` Tim Behrendsen
1996-08-08 0:00 ` Peter Seebach
1996-08-08 0:00 ` Randy Kaelber
1996-08-09 0:00 ` Chris Sonnack
1996-08-10 0:00 ` Tim Behrendsen
1996-08-11 0:00 ` Dan Pop
1996-08-12 0:00 ` Chris Sonnack
1996-08-15 0:00 ` Bob Hoffmann
1996-08-12 0:00 ` Tim Behrendsen
1996-08-11 0:00 ` Chris Sonnack
1996-08-09 0:00 ` J. Blustein
1996-08-11 0:00 ` Peter Seebach
1996-08-09 0:00 ` Dan Pop
1996-08-11 0:00 ` Mark Wooding
1996-08-19 0:00 ` James Youngman
1996-08-11 0:00 ` Tim Behrendsen
1996-08-11 0:00 ` Dan Pop
1996-08-13 0:00 ` Tim Behrendsen
1996-08-13 0:00 ` Giuliano Carlini
1996-08-14 0:00 ` Dan Pop
1996-08-14 0:00 ` Tim Behrendsen
1996-08-16 0:00 ` Dik T. Winter
1996-08-12 0:00 ` Peter Seebach
1996-08-13 0:00 ` Tim Behrendsen
1996-08-18 0:00 ` Sam B. Siegel
1996-08-19 0:00 ` Dan Pop
1996-08-08 0:00 ` Christopher R Volpe
1996-08-07 0:00 ` Peter Seebach
1996-08-08 0:00 ` Tim Behrendsen
1996-08-08 0:00 ` Peter Seebach
1996-08-08 0:00 ` Tim Behrendsen
1996-08-08 0:00 ` Peter Seebach
1996-08-14 0:00 ` Richard A. O'Keefe
1996-08-16 0:00 ` Tim Behrendsen
1996-08-20 0:00 ` Richard A. O'Keefe
1996-08-20 0:00 ` Alan Bowler
1996-08-21 0:00 ` Tim Behrendsen
1996-08-22 0:00 ` Bengt Richter
1996-08-22 0:00 ` Tim Behrendsen
1996-08-31 0:00 ` Bengt Richter
1996-09-01 0:00 ` Maurice M. Carey IV
1996-08-26 0:00 ` Richard A. O'Keefe
1996-08-26 0:00 ` Tim Behrendsen
1996-08-29 0:00 ` Richard A. O'Keefe
1996-08-29 0:00 ` Craig Franck
[not found] ` <01bb95ba$9dfed580$496700cf@ljelmore.montana>
1996-08-30 0:00 ` Steve Heller
1996-08-31 0:00 ` Clayton Weaver
1996-08-30 0:00 ` system
1996-08-31 0:00 ` Kenneth Mays
1996-09-01 0:00 ` Tim Behrendsen
1996-08-26 0:00 ` Mark Wooding
1996-08-30 0:00 ` Kaz Kylheku
1996-08-30 0:00 ` Richard A. O'Keefe
1996-08-30 0:00 ` Peter Seebach
1996-09-03 0:00 ` Lawrence Kirby
1996-09-01 0:00 ` Joe Keane
1996-09-04 0:00 ` Richard A. O'Keefe
1996-09-03 0:00 ` Arkady Belousov
1996-08-26 0:00 ` madscientist
1996-08-29 0:00 ` Richard A. O'Keefe
1996-08-31 0:00 ` Tanmoy Bhattacharya
1996-09-04 0:00 ` Tom Payne
1996-09-04 0:00 ` Patrick Horgan
1996-09-05 0:00 ` Richard A. O'Keefe
1996-09-05 0:00 ` deafen
1996-08-09 0:00 ` Chris Sonnack
1996-08-08 0:00 ` telnet user
1996-08-09 0:00 ` Tim Behrendsen
1996-08-09 0:00 ` Ed Hook
1996-08-09 0:00 ` Mike Rubenstein
1996-08-09 0:00 ` Tim Behrendsen
1996-08-10 0:00 ` Mike Rubenstein
1996-08-12 0:00 ` Tim Behrendsen
1996-08-12 0:00 ` Mike Rubenstein
1996-08-12 0:00 ` Mark Wooding
1996-08-13 0:00 ` Mike Rubenstein
1996-08-15 0:00 ` Richard A. O'Keefe
1996-08-12 0:00 ` Tim Behrendsen
1996-08-13 0:00 ` Mike Rubenstein
1996-08-13 0:00 ` Tim Behrendsen
1996-08-13 0:00 ` Giuliano Carlini
1996-08-14 0:00 ` Tim Behrendsen
1996-08-15 0:00 ` Mike Rubenstein
[not found] ` <32 <01bb8923$e1d34280$87ee6fce@timpent.airshields.com>
1996-08-14 0:00 ` Peter Seebach
1996-08-14 0:00 ` Tim Behrendsen
1996-08-14 0:00 ` Peter Seebach
1996-08-12 0:00 ` Bob Kitzberger
1996-08-22 0:00 ` Patrick Horgan
1996-08-23 0:00 ` Steve Heller
1996-08-08 0:00 ` Teaching sorts [was Re: What's the best language to start with?] Robert I. Eachus
1996-08-09 0:00 ` Robert Dewar
1996-08-10 0:00 ` Lawrence Kirby
1996-08-10 0:00 ` Al Aab
1996-08-12 0:00 ` Steve Heller
1996-08-12 0:00 ` Robert Dewar
1996-08-16 0:00 ` Steve Heller
1996-08-16 0:00 ` Robert Dewar
1996-08-18 0:00 ` Steve Heller
1996-08-18 0:00 ` Robert Dewar
1996-08-18 0:00 ` Steve Heller
1996-08-18 0:00 ` Robert Dewar
1996-08-20 0:00 ` Steve Heller
1996-08-16 0:00 ` Adam Beneschan
1996-08-18 0:00 ` Steve Heller
1996-08-18 0:00 ` Jeff Dege
1996-08-18 0:00 ` Robert Dewar
1996-08-16 0:00 ` Szu-Wen Huang
1996-08-17 0:00 ` Robert Dewar
1996-08-20 0:00 ` Szu-Wen Huang
1996-08-20 0:00 ` Dann Corbit
1996-08-21 0:00 ` Tim Behrendsen
1996-08-21 0:00 ` Dann Corbit
1996-08-22 0:00 ` Richard A. O'Keefe
1996-08-22 0:00 ` Szu-Wen Huang
1996-08-23 0:00 ` Richard A. O'Keefe
1996-08-25 0:00 ` Robert Dewar
1996-08-21 0:00 ` Dik T. Winter
1996-08-21 0:00 ` Tim Behrendsen
1996-08-21 0:00 ` Pete Becker
1996-08-22 0:00 ` Szu-Wen Huang
1996-08-22 0:00 ` Pete Becker
1996-08-22 0:00 ` Robert Dewar
1996-08-21 0:00 ` Tanmoy Bhattacharya [this message]
1996-08-22 0:00 ` Dann Corbit
1996-08-22 0:00 ` Mike Rubenstein
1996-08-21 0:00 ` Matt Austern
1996-08-21 0:00 ` Tim Behrendsen
1996-08-22 0:00 ` Robert Dewar
1996-08-24 0:00 ` Joe Keane
1996-08-22 0:00 ` Tanmoy Bhattacharya
1996-08-21 0:00 ` Tanmoy Bhattacharya
1996-08-21 0:00 ` Tim Behrendsen
1996-08-22 0:00 ` Robert Dewar
1996-08-22 0:00 ` Mike Rubenstein
1996-08-21 0:00 ` Adam Beneschan
1996-08-22 0:00 ` Christian Bau
1996-08-22 0:00 ` (topic change on) Teaching sorts Marcus H. Mendenhall
1996-08-27 0:00 ` Ralph Silverman
1996-08-22 0:00 ` Teaching sorts [was Re: What's the best language to start with?] Larry Kilgallen
1996-08-23 0:00 ` Tim Hollebeek
1996-08-24 0:00 ` Robert Dewar
1996-08-24 0:00 ` Robert Dewar
1996-08-23 0:00 ` Andrew Koenig
1996-08-22 0:00 ` Andrew Koenig
1996-08-24 0:00 ` Robert Dewar
1996-08-17 0:00 ` Robert Dewar
1996-08-18 0:00 ` Steve Heller
1996-08-21 0:00 ` Matt Austern
1996-08-23 0:00 ` Tanmoy Bhattacharya
1996-08-23 0:00 ` Adam Beneschan
1996-08-14 0:00 ` Stephen Baynes
1996-08-14 0:00 ` Robert Dewar
1996-08-14 0:00 ` Robert Dewar
1996-08-16 0:00 ` Dik T. Winter
1996-08-16 0:00 ` Joe Foster
1996-08-18 0:00 ` Glenn Rhoads
1996-08-19 0:00 ` Stephen Baynes
1996-08-19 0:00 ` Robert Dewar
1996-08-19 0:00 ` Robert Dewar
1996-08-19 0:00 ` Richard A. O'Keefe
[not found] ` <dewar.840491732@schonberg>
1996-08-19 0:00 ` Robert Dewar
1996-08-22 0:00 ` Stephen Baynes
1996-08-27 0:00 ` Richard A. O'Keefe
1996-08-13 0:00 ` Robert I. Eachus
1996-08-14 0:00 ` Robert Dewar
1996-08-15 0:00 ` Tom Payne
1996-08-13 0:00 ` Robert I. Eachus
1996-08-13 0:00 ` Lawrence Kirby
1996-08-14 0:00 ` Robert Dewar
1996-08-14 0:00 ` Robert I. Eachus
1996-08-15 0:00 ` Robert Dewar
1996-08-15 0:00 ` Blair Phillips
1996-08-27 0:00 ` What's the best language to start with? [was: Re: Should I learn C or Pascal?] Tanmoy Bhattacharya
1996-08-29 0:00 ` Robert I. Eachus
1996-08-30 0:00 ` Steve Heller
1996-08-30 0:00 ` Tanmoy Bhattacharya
1996-08-07 0:00 ` What's the best language to start with Ian Ward
1996-08-08 0:00 ` Tim Behrendsen
1996-08-09 0:00 ` Robert Dewar
1996-08-11 0:00 ` What's the best language to start with? [was: Re: Should I learn C or Pascal?] Jerone A. Bowers
1996-08-06 0:00 ` Fergus Henderson
1996-08-07 0:00 ` Tim Behrendsen
1996-08-08 0:00 ` Thomas Hood
1996-08-09 0:00 ` Tim Behrendsen
1996-08-17 0:00 ` Lawrence Kirby
1996-08-17 0:00 ` Tim Behrendsen
1996-08-19 0:00 ` Bob Gilbert
1996-08-19 0:00 ` Tim Behrendsen
1996-08-19 0:00 ` Tim Hollebeek
1996-08-20 0:00 ` Tim Behrendsen
1996-08-20 0:00 ` Bob Gilbert
1996-08-21 0:00 ` Tim Behrendsen
1996-08-22 0:00 ` Bob Gilbert
1996-08-22 0:00 ` Tim Behrendsen
1996-09-04 0:00 ` Lawrence Kirby
1996-09-04 0:00 ` Tim Behrendsen
1996-09-06 0:00 ` Bob Gilbert
1996-09-06 0:00 ` Tim Behrendsen
1996-09-09 0:00 ` Bob Gilbert
1996-09-11 0:00 ` Tim Behrendsen
1996-09-10 0:00 ` Jon S Anthony
1996-09-11 0:00 ` Richard A. O'Keefe
1996-09-10 0:00 ` Richard A. O'Keefe
1996-09-10 0:00 ` Kaz Kylheku
1996-09-11 0:00 ` Bob Gilbert
1996-09-11 0:00 ` Jon S Anthony
1996-09-11 0:00 ` Jon S Anthony
1996-09-05 0:00 ` Mark Wooding
1996-09-06 0:00 ` Bob Cousins
1996-09-06 0:00 ` Tim Behrendsen
1996-09-07 0:00 ` Craig Franck
1996-09-08 0:00 ` Tim Behrendsen
1996-09-08 0:00 ` Craig Franck
1996-09-09 0:00 ` Tim Behrendsen
1996-09-10 0:00 ` Richard A. O'Keefe
1996-09-10 0:00 ` Tim Behrendsen
1996-09-11 0:00 ` John Burdick
1996-09-13 0:00 ` Bengt Richter
1996-09-14 0:00 ` Craig Franck
1996-09-06 0:00 ` Robert I. Eachus
1996-09-06 0:00 ` Tim Behrendsen
1996-09-11 0:00 ` Jon S Anthony
1996-09-11 0:00 ` Jon S Anthony
1996-09-11 0:00 ` Craig Franck
1996-09-11 0:00 ` Tim Behrendsen
1996-09-17 0:00 ` George
1996-09-24 0:00 ` Joel VanLaven
1996-09-27 0:00 ` Tom Payne
1996-09-28 0:00 ` Tim Behrendsen
1996-09-27 0:00 ` Dann Corbit
1996-09-11 0:00 ` Richard A. O'Keefe
1996-09-11 0:00 ` Tim Behrendsen
1996-09-12 0:00 ` Richard A. O'Keefe
1996-09-13 0:00 ` Tim Behrendsen
1996-09-13 0:00 ` Richard A. O'Keefe
1996-09-18 0:00 ` Tim Behrendsen
1996-09-19 0:00 ` Richard A. O'Keefe
1996-09-12 0:00 ` Peter Seebach
1996-09-18 0:00 ` Tim Behrendsen
1996-09-17 0:00 ` George
1996-09-19 0:00 ` Tim Behrendsen
1996-09-24 0:00 ` Matthew M. Lih
1996-09-25 0:00 ` Richard A. O'Keefe
1996-09-26 0:00 ` Mark Wooding
1996-09-25 0:00 ` Bjarne Stroustrup
1996-09-26 0:00 ` Bengt Richter
1996-09-28 0:00 ` Dan Pop
1996-09-26 0:00 ` Jon S Anthony
1996-09-26 0:00 ` Dann Corbit
1996-09-27 0:00 ` Craig Franck
1996-09-27 0:00 ` Bob Cousins
1996-09-27 0:00 ` Jay Martin
1996-09-27 0:00 ` Kent Budge
1996-09-27 0:00 ` George Haddad
1996-09-27 0:00 ` George Haddad
1996-09-27 0:00 ` George Haddad
1996-09-27 0:00 ` George Haddad
1996-09-27 0:00 ` George Haddad
1996-09-28 0:00 ` Matthew Heaney
1996-09-28 0:00 ` Steve Heller
1996-10-01 0:00 ` DJ Kindberg
1996-09-27 0:00 ` Tim Behrendsen
1996-09-30 0:00 ` Art Schwarz
1996-09-28 0:00 ` Jon S Anthony
1996-09-18 0:00 ` Jon S Anthony
1996-09-26 0:00 ` Jon S Anthony
1996-10-01 0:00 ` Andrew Gierth
1996-08-22 0:00 ` Bengt Richter
1996-08-22 0:00 ` Tim Behrendsen
1996-08-23 0:00 ` Larry J. Elmore
1996-08-22 0:00 ` Frank Manning
1996-08-31 0:00 ` Bengt Richter
1996-08-31 0:00 ` Frank Manning
1996-08-31 0:00 ` Frank Manning
1996-09-02 0:00 ` deafen
1996-09-03 0:00 ` Frank Manning
1996-09-03 0:00 ` Steve Howard
1996-09-03 0:00 ` Bob Kitzberger
1996-09-03 0:00 ` Tim Behrendsen
1996-09-03 0:00 ` Phil Barnett
1996-08-08 0:00 ` Stephen M O'Shaughnessy
[not found] ` <01bb846d$ <Dvtnon.I49@most.fw.hac.com>
1996-08-09 0:00 ` Tim Behrendsen
1996-08-09 0:00 ` Stephen M O'Shaughnessy
1996-08-09 0:00 ` Tim Behrendsen
1996-08-12 0:00 ` Robert I. Eachus
1996-08-05 0:00 ` Chris Sonnack
1996-08-06 0:00 ` Stephen M O'Shaughnessy
1996-08-13 0:00 ` Chris Sonnack
1996-08-16 0:00 ` Steve Heller
1996-08-16 0:00 ` John Hobson
1996-07-31 0:00 ` Patrick Horgan
1996-07-31 0:00 ` AJ Musgrove
1996-08-01 0:00 ` Sam Harris
1996-08-02 0:00 ` Eric W. Nikitin
1996-08-01 0:00 ` Tim Hollebeek
1996-08-01 0:00 ` Ken Pizzini
1996-08-03 0:00 ` Raffael Cavallaro
1996-08-05 0:00 ` Chris Sonnack
1996-08-08 0:00 ` William Clodius
1996-08-11 0:00 ` Fergus Henderson
1996-08-11 0:00 ` Dik T. Winter
1996-08-08 0:00 ` William Clodius
1996-08-13 0:00 ` Ole-Hjalmar Kristensen FOU.TD/DELAB
1996-08-14 0:00 ` Richard A. O'Keefe
1996-08-15 0:00 ` Teaching sorts [was Re: What's the best language to start with?] Norman H. Cohen
1996-08-16 0:00 ` Steve Heller
1996-08-19 0:00 ` Ted Dennison
1996-08-23 0:00 ` Richard A. O'Keefe
1996-08-23 0:00 ` Ted Dennison
1996-08-24 0:00 ` Robert Dewar
1996-08-27 0:00 ` Richard A. O'Keefe
1996-09-02 0:00 ` Lawrence Kirby
1996-07-28 0:00 ` What's the best language to start with? [was: Re: Should I learn C or Pascal?] Robert Dewar
1996-07-29 0:00 ` Tim Behrendsen
1996-07-30 0:00 ` Paul Campbell
1996-07-30 0:00 ` Robert Dewar
1996-08-02 0:00 ` Tim Behrendsen
1996-08-03 0:00 ` Peter Seebach
1996-08-04 0:00 ` Alf P. Steinbach
1996-08-04 0:00 ` Peter Seebach
1996-08-04 0:00 ` Jerry van Dijk
1996-08-05 0:00 ` Tim Behrendsen
1996-08-04 0:00 ` Peter Seebach
1996-08-05 0:00 ` Chris Sonnack
1996-08-05 0:00 ` Peter Seebach
1996-08-07 0:00 ` Tom Watson
1996-08-05 0:00 ` Tim Hollebeek
1996-08-10 0:00 ` Mike Rubenstein
1996-08-06 0:00 ` Tim Behrendsen
1996-08-03 0:00 ` Patrick Horgan
1996-08-04 0:00 ` Kurt E. Huhner
1996-07-30 0:00 ` What's the best language to start with? [was: Re: Should I learn TRAN PHAN ANH
1996-07-31 0:00 ` What's the best language to start with? [was: Re: Should I learn C or Pascal?] Arne W. Flones
1996-08-02 0:00 ` David Wheeler
1996-08-02 0:00 ` Peter Seebach
1996-08-02 0:00 ` Gary M. Greenberg
1996-08-03 0:00 ` Alf P. Steinbach
1996-08-02 0:00 ` Peter Seebach
1996-08-05 0:00 ` Chris Sonnack
1996-08-05 0:00 ` Peter Seebach
1996-08-06 0:00 ` What's the best language to start with? [was: Re: Should I learn C or Pasca StHeller
1996-08-06 0:00 ` Robert Dewar
1996-08-06 0:00 ` What's the best language to start with? [was: Re: Should I learn C or Pascal?] Alf P. Steinbach
1996-08-06 0:00 ` Conrad Herrmann
1996-08-06 0:00 ` Robert I. Eachus
1996-07-29 0:00 ` Byron B. Kauffman
1996-07-30 0:00 ` Alan Peake
[not found] ` <dewar. <peake.206.002D549F@dstos3.dsto.gov.au>
1996-07-31 0:00 ` Stephen M O'Shaughnessy
1996-08-02 0:00 ` Tim Behrendsen
1996-08-05 0:00 ` Mark McKinney
1996-08-05 0:00 ` Mark McKinney
1996-08-05 0:00 ` Mark McKinney
1996-07-31 0:00 ` Tim Behrendsen
1996-07-31 0:00 ` P. Cnudde VH14 (8218)
1996-07-31 0:00 ` Nicolas Devillard
1996-08-02 0:00 ` Matt Austern
1996-08-15 0:00 ` Lawrence Kirby
1996-07-20 0:00 ` Should I learn C or Pascal? Robert Dewar
1996-07-22 0:00 ` TRAN PHAN ANH
1996-07-23 0:00 ` Ken Garlington
1996-07-20 0:00 ` Andy Askey
1996-07-20 0:00 ` steidl
1996-07-21 0:00 ` Andy Askey
1996-07-22 0:00 ` Stephen M O'Shaughnessy
1996-07-23 0:00 ` TRAN PHAN ANH
1996-07-18 0:00 ` Walter B. Hollman Sr.
1996-07-18 0:00 ` Patrick Horgan
1996-07-18 0:00 ` Jason Alan Turnage
1996-07-19 0:00 ` Vic Metcalfe
1996-07-19 0:00 ` Robert Dewar
1996-07-20 0:00 ` steved
1996-07-19 0:00 ` Peter Seebach
1996-07-20 0:00 ` Robert Dewar
1996-07-22 0:00 ` steidl
1996-07-22 0:00 ` Stephen M O'Shaughnessy
1996-07-23 0:00 ` Richard A. O'Keefe
1996-07-23 0:00 ` Michael Ickes
1996-07-25 0:00 ` Andy Askey
1996-07-24 0:00 ` system
1996-07-20 0:00 ` Jon Bell
1996-07-20 0:00 ` Andy Askey
1996-07-23 0:00 ` Ralph Silverman
1996-07-18 0:00 ` Robert Dewar
1996-07-19 0:00 ` Billy Chambless
1996-07-19 0:00 ` Reto Koradi
1996-07-23 0:00 ` TRAN PHAN ANH
1996-07-19 0:00 ` Scott McMahan - Softbase Systems
1996-07-20 0:00 ` steidl
1996-07-20 0:00 ` Tim Behrendsen
1996-07-21 0:00 ` Rich Maggio
1996-07-21 0:00 ` Robert Dewar
1996-07-22 0:00 ` Ralph Silverman
1996-07-23 0:00 ` Tim Behrendsen
1996-07-19 0:00 ` Andrew Gierth
1996-07-18 0:00 ` Carlos DeAngulo
1996-07-18 0:00 ` Robert Dewar
1996-07-19 0:00 ` Jon Bell
1996-07-22 0:00 ` Tim Oxler
1996-07-22 0:00 ` Stig Norland
1996-07-22 0:00 ` Robert Dewar
1996-07-30 0:00 ` Tim Behrendsen
1996-07-31 0:00 ` Patrick Horgan
1996-07-22 0:00 ` Janus
[not found] ` <01bb7588$236982e0$7b91f780@deangulo>
1996-07-19 0:00 ` Robert Dewar
1996-07-20 0:00 ` steidl
[not found] ` <01bb7591$83087d60$87ee6fce@timpent.airshields.com>
1996-07-19 0:00 ` Craig Franck
1996-07-19 0:00 ` johnf
1996-07-19 0:00 ` Jeremy Nelson
1996-07-19 0:00 ` Jason Alan Turnage
1996-07-19 0:00 ` Robert Dewar
1996-07-20 0:00 ` Jon Bell
1996-07-20 0:00 ` Robert Dewar
1996-07-21 0:00 ` Alexander Vrenios
1996-07-21 0:00 ` Steve Tate
1996-07-21 0:00 ` Robert Dewar
1996-07-21 0:00 ` Phil Howard
1996-07-21 0:00 ` Robert Dewar
1996-07-22 0:00 ` Steve Tate
1996-07-22 0:00 ` Stephen M O'Shaughnessy
1996-07-25 0:00 ` ++ robin
1996-07-20 0:00 ` TRAN PHAN ANH
1996-07-22 0:00 ` Ralph Silverman
1996-07-20 0:00 ` Crash
1996-07-20 0:00 ` Robert Dewar
1996-07-23 0:00 ` Ralph Silverman
1996-07-22 0:00 ` Stephen M O'Shaughnessy
1996-07-22 0:00 ` Jeremy Nelson
1996-07-22 0:00 ` Stephen M O'Shaughnessy
1996-07-20 0:00 ` Tim Behrendsen
1996-07-22 0:00 ` Ralph Silverman
1996-07-23 0:00 ` Joe Gwinn
1996-07-24 0:00 ` John A Hughes
1996-07-24 0:00 ` Theodore E. Dennison
1996-07-23 0:00 ` John A Hughes
1996-07-19 0:00 ` Dirk Dickmanns
1996-07-23 0:00 ` Richard A. O'Keefe
1996-07-16 0:00 ` Darin Johnson
1996-07-24 0:00 ` Ralph Silverman
1996-07-17 0:00 ` Aron Felix Gurski
1996-07-19 0:00 ` Andrew Gierth
1996-07-19 0:00 ` Andrew Gierth
1996-07-19 0:00 ` Andrew Gierth
1996-07-21 0:00 ` Wayne
1996-07-21 0:00 ` Laurent Guerby
1996-07-22 0:00 ` Stephen M O'Shaughnessy
1996-07-22 0:00 ` Darin Johnson
1996-07-22 0:00 ` Darin Johnson
1996-07-23 0:00 ` Darin Johnson
1996-07-24 0:00 ` Andrew J Steinbach
1996-07-24 0:00 ` John A Hughes
1996-07-24 0:00 ` Jon Bell
1996-07-24 0:00 ` system
1996-07-24 0:00 ` Ralph Silverman
1996-07-24 0:00 ` TRAN PHAN ANH
1996-07-24 0:00 ` Michael Feldman
1996-07-24 0:00 ` Jon S Anthony
1996-07-24 0:00 ` Darin Johnson
1996-07-25 0:00 ` Andy Askey
1996-07-26 0:00 ` Mark Eissler
1996-08-02 0:00 ` Patrick Horgan
1996-08-04 0:00 ` Gary M. Greenberg
[not found] ` <4u76ej$7s9@newsbf02.news.aol.com>
1996-08-06 0:00 ` Ralph Silverman
1996-08-12 0:00 ` Patrick Horgan
1996-08-13 0:00 ` Ralph Silverman
1996-08-13 0:00 ` Darin Johnson
1996-08-13 0:00 ` What's the best language to learn? [was Re: Should I learn C or Pascal?] Tim Behrendsen
1996-08-14 0:00 ` Gabor Egressy
1996-08-15 0:00 ` Robert Dewar
1996-08-17 0:00 ` Lawrence Kirby
1996-08-17 0:00 ` Robert Dewar
1996-08-20 0:00 ` Lawrence Kirby
1996-08-16 0:00 ` Mark Wooding
1996-08-17 0:00 ` Dan Pop
1996-08-17 0:00 ` Tim Behrendsen
1996-08-17 0:00 ` Robert Dewar
1996-08-17 0:00 ` Dan Pop
1996-08-18 0:00 ` Mark Wooding
1996-08-20 0:00 ` Peter Seebach
1996-08-21 0:00 ` Szu-Wen Huang
1996-08-21 0:00 ` Adam Beneschan
1996-08-21 0:00 ` Tim Behrendsen
1996-08-17 0:00 ` Peter Seebach
1996-08-18 0:00 ` Tim Behrendsen
1996-08-21 0:00 ` Tanmoy Bhattacharya
1996-08-30 0:00 ` Goto considered really harmful Patrick Horgan
1996-09-04 0:00 ` Dennison
1996-08-14 0:00 ` What's the best language to learn? [was Re: Should I learn C or Pascal?] Peter Seebach
1996-08-14 0:00 ` Tim Behrendsen
1996-08-14 0:00 ` Robert Dewar
1996-08-14 0:00 ` Dan Pop
1996-08-14 0:00 ` Robert Dewar
1996-08-14 0:00 ` Tim Behrendsen
1996-08-15 0:00 ` Joe Foster
1996-08-14 0:00 ` Peter Seebach
1996-08-14 0:00 ` Tim Behrendsen
1996-08-14 0:00 ` Peter Seebach
1996-08-15 0:00 ` Robert Dewar
1996-08-16 0:00 ` Joe Foster
1996-08-18 0:00 ` Tim Behrendsen
1996-08-20 0:00 ` James Youngman
1996-08-21 0:00 ` Szu-Wen Huang
1996-08-15 0:00 ` Bob Gilbert
1996-08-15 0:00 ` Bob Gilbert
1996-08-18 0:00 ` Tim Behrendsen
1996-08-15 0:00 ` DAVID A MOLNAR
1996-08-16 0:00 ` Dr. Richard Botting
1996-08-18 0:00 ` Tim Behrendsen
1996-08-21 0:00 ` Szu-Wen Huang
1996-08-21 0:00 ` Tim Behrendsen
1996-08-22 0:00 ` Mark Wooding
1996-08-23 0:00 ` Bengt Richter
1996-08-23 0:00 ` Clayton Weaver
1996-08-16 0:00 ` Bob Gilbert
1996-08-17 0:00 ` Tim Behrendsen
1996-08-18 0:00 ` Robert Dewar
1996-08-18 0:00 ` Tim Behrendsen
1996-08-26 0:00 ` Patrick Horgan
1996-08-27 0:00 ` Alan Peake
1996-08-27 0:00 ` Steve Heller
1996-08-28 0:00 ` Robert Dewar
1996-08-28 0:00 ` Tom Watson
1996-08-28 0:00 ` Robert Dewar
1996-08-30 0:00 ` Alan Peake
1996-08-31 0:00 ` Robert Dewar
1996-09-03 0:00 ` Alan Peake
1996-09-07 0:00 ` Robert Dewar
1996-09-07 0:00 ` .
1996-08-29 0:00 ` Darin Johnson
1996-08-19 0:00 ` John Hobson
1996-08-19 0:00 ` Tim Behrendsen
1996-08-19 0:00 ` John Hobson
1996-08-20 0:00 ` Szu-Wen Huang
1996-08-27 0:00 ` Richard A. O'Keefe
1996-08-23 0:00 ` Alan Bowler
1996-08-21 0:00 ` What's the best language to learn? [any language except Ada] Bill Mackay
1996-08-22 0:00 ` Robert Dewar
1996-08-23 0:00 ` Larry J. Elmore
1996-08-22 0:00 ` Stephen M O'Shaughnessy
1996-08-24 0:00 ` Alan Brain
1996-08-15 0:00 ` Should I learn C or Pascal? Richard A. O'Keefe
1996-08-17 0:00 ` Lawrence Kirby
1996-08-18 0:00 ` Ken Pizzini
1996-08-19 0:00 ` Richard A. O'Keefe
1996-08-23 0:00 ` Joe Keane
1996-08-17 0:00 ` Mike Rubenstein
1996-08-17 0:00 ` Alexander J Russell
1996-08-16 0:00 ` Dr E. Buxbaum
1996-08-16 0:00 ` Mike Rubenstein
1996-08-16 0:00 ` Lawrence Kirby
1996-08-17 0:00 ` Paul Hsieh
1996-08-17 0:00 ` Mike Rubenstein
1996-08-19 0:00 ` Richard A. O'Keefe
1996-08-20 0:00 ` Mike Rubenstein
1996-08-22 0:00 ` Richard A. O'Keefe
1996-08-22 0:00 ` Mike Rubenstein
1996-08-20 0:00 ` Paul Schlyter
1996-08-20 0:00 ` Mike Rubenstein
1996-08-21 0:00 ` James Youngman
1996-08-22 0:00 ` TRAN PHAN ANH
1996-08-22 0:00 ` Dr E. Buxbaum
1996-08-27 0:00 ` Jeffrey C. Dege
1996-08-27 0:00 ` Craig Franck
1996-08-27 0:00 ` Ted Dennison
1996-08-27 0:00 ` John Hobson
1996-08-27 0:00 ` Ted Dennison
1996-08-27 0:00 ` Steve Heller
1996-08-27 0:00 ` Bob Cousins
1996-08-28 0:00 ` Robert Dewar
1996-09-01 0:00 ` Patrick Horgan
1996-09-12 0:00 ` Delete - Don't Bother to Read This Charles H. Sampson
1996-08-16 0:00 ` Should I learn C or Pascal? Darin Johnson
1996-08-16 0:00 ` What's the best language to learn? [was Re: Should I learn C or Pascal?] Darin Johnson
1996-08-16 0:00 ` Robert Dewar
1996-08-16 0:00 ` system
1996-08-20 0:00 ` Should I learn C or Pascal? Darin Johnson
1996-08-21 0:00 ` What's the best language to learn? [was Re: Should I learn C or Pascal?] Darin Johnson
1996-08-22 0:00 ` What's the best language to learn? [any language except Ada] Jon S Anthony
1996-08-23 0:00 ` Darin Johnson
1996-08-25 0:00 ` Robert Dewar
1996-08-24 0:00 ` Jon S Anthony
1996-08-05 0:00 ` Should I learn C or Pascal? Sherwin Anthony Sequeira
1996-07-25 0:00 ` ++ robin
1996-07-25 0:00 ` ++ robin
1996-07-30 0:00 ` Robert Barnes
1996-07-30 0:00 ` Rob(t.) Brannan
1996-08-01 0:00 ` ++ robin
1996-08-01 0:00 ` Ralph Silverman
1996-08-06 0:00 ` ++ robin
1996-08-01 0:00 ` Tony Konashenok
1996-08-04 0:00 ` Lawrence Kirby
1996-08-09 0:00 ` Verne Arase
1996-07-25 0:00 ` ++ robin
1996-07-31 0:00 ` What's the best language to start with? [was: Re: Should I learn C or Pascal?] Darin Johnson
1996-08-01 0:00 ` Tim Behrendsen
1996-08-01 0:00 ` Stephen M O'Shaughnessy
1996-08-03 0:00 ` Tim Behrendsen
1996-08-06 0:00 ` Stephen M O'Shaughnessy
1996-08-05 0:00 ` Patrick Horgan
1996-08-06 0:00 ` Szu-Wen Huang
1996-08-06 0:00 ` Dan Pop
1996-08-08 0:00 ` steidl
1996-07-31 0:00 ` Darin Johnson
1996-08-02 0:00 ` Alan Peake
1996-08-01 0:00 ` Andy Hardy
1996-08-01 0:00 ` Stefan 'Stetson' Skoglund
1996-08-05 0:00 ` Stephen M O'Shaughnessy
1996-08-06 0:00 ` Bob Gilbert
1996-08-07 0:00 ` Stephen M O'Shaughnessy
1996-08-09 0:00 ` Bob Gilbert
1996-08-06 0:00 ` Patrick Horgan
1996-08-07 0:00 ` Fergus Henderson
1996-08-07 0:00 ` Tim Behrendsen
1996-08-08 0:00 ` Szu-Wen Huang
1996-08-08 0:00 ` Tim Behrendsen
1996-08-08 0:00 ` Christopher R Volpe
1996-08-08 0:00 ` Peter Seebach
1996-08-08 0:00 ` Tim Behrendsen
1996-08-08 0:00 ` Peter Seebach
1996-08-09 0:00 ` Tim Behrendsen
1996-08-09 0:00 ` Peter Seebach
1996-08-15 0:00 ` James_Rogers
1996-08-17 0:00 ` Tim Behrendsen
1996-08-10 0:00 ` Mike Rubenstein
1996-08-10 0:00 ` Peter Seebach
1996-08-11 0:00 ` Craig Franck
1996-08-08 0:00 ` Szu-Wen Huang
1996-08-08 0:00 ` Tim Behrendsen
1996-08-09 0:00 ` Szu-Wen Huang
1996-08-09 0:00 ` Tim Behrendsen
1996-08-10 0:00 ` Szu-Wen Huang
1996-08-11 0:00 ` Tim Behrendsen
1996-08-09 0:00 ` some days weren't there at all
1996-08-10 0:00 ` Mike Rubenstein
1996-08-11 0:00 ` Szu-Wen Huang
1996-08-17 0:00 ` Richard Chiu
1996-09-04 0:00 ` Lawrence Kirby
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