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Poll
Yes?
Yes, I know. 11%
Yes, and thank you for the reminder. 17%
Yes, thank you for bringing this matter to my attention, I will be sure to keep it in mind if I ever need to make use of this arcane branch of mathematics. 23%
No, I am an unapologetic and unwashed brute who uses the exclamation point to express negation. 47%

Votes: 17

 A Formal reminder.

 Author:  Topic:  Posted:
Dec 20, 2001
 Comments:
It has come to my attention that several participants at the adequacy have been attempting to intersperse their writings with brief examples from the branch of mathematics known as Formal Logic.
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Deletion Notice
In these illustrative examples, some have mistakenly been using the tilde ("~") to express negation, and a few ignorant brutes have been using the exclamation point ("!") as well. The latter I will not deign to address, as it is clearly an abomination, but the tilde requires some discussion.

As anyone familiar with mathematical journals or better textbooks can tell you, the negation symbol ("¬") is quite distict from the tilde. The tilde, a mere punctuation mark, meaningless on its own, was originally introduced into some inferior mathematical literature solely as a consequence of inadequate typesetting capabilities.

The days of such technical problems are long gone; if you wish to use the negation symbol today, all you need to do is locate the appropriate key or switch on your writing mechanism, and activate it. I will illustrate with an example, but first I would like to remind everyone that mathematical examples should be clearly set apart from prose using appropriate spacing. The occasional exception will of course crop up, to the amusement of all, but please try to be considerate, and keep the sensibilities of your readers in mind. Now, we will illustrate with that old chestnut, the contrapositive:

    if a then b <-> if ¬b then ¬a

I am sure this reminder is not necessary for most of you; for the rest, please do not take this as an insult; after all, anyone might lose sight of details like this from time to time.

       
Tweet

Your vigilance is gratifying. (none / 0) (#1)
by elenchos on Thu Dec 20th, 2001 at 04:33:02 PM PST
Though, like all real USians, I deplore the horrific loss of life and property (but mostly life of course) from the recent hacker-aided terrorist attacks on USia, it is some small consolation that a few sharp-eyed members of the public have become more aware of the activities of terrorists and terrorist-like Internet posters. We may have lost our tall buildings, but we have also buried the hippie let-it-all-hang-out laxity that benighted our people for the last three and three-tenths decades, and replaced it with a newfound sense of responsibility to react strongly to each and every threat to freedom represented by these deviants.

Thank you, Slave.


I do, I do, I do
--Bikini Kill

 
math (none / 0) (#2)
by motherfuckin spork on Thu Dec 20th, 2001 at 07:33:00 PM PST
I deplore math. I despise it. Not because it is difficult, but because it is overblown and has been made into a quasi-philosophical conundrum by overbearing, overzealous windbags with far too much time on their hands. Unlike abstract mathematicians or other such nonsense, I actually live and function in the real world. If I wish to say that something is not something else, then I say so, without the use of some foolish looking equation that words suffice, and often excel, at describing.


I am not who you think I am.

Can we talk about your feelings, then? (5.00 / 1) (#3)
by RobotSlave on Thu Dec 20th, 2001 at 07:52:20 PM PST
Personally, I neither love nor hate maths. Mathematics is an eccentric field of human endeavor, one which has produced a few useful tools, one must concede, but it is far from an emotionally compelling discipline, let alone the edifice of political or philisophical ideology that you seem to make it out to be.

The question, then, is why are you so angry about mathematics? Has a mathematician hurt you in some way, or spurned your love, perhaps? Or do you fear even the false semblance of certainty that mathematics might represent to you? Do you crave the abolition of authority? Were your parents overbearing? I am but groping in the dark here, but I am fascinated; any additional information you can offer would be most welcome.


© 2002, RobotSlave. You may not reproduce this material, in whole or in part, without written permission of the owner.

 
Give me a break (none / 0) (#5)
by Anonymous Reader on Thu Dec 20th, 2001 at 08:34:40 PM PST
If you can honestly say that Cantor's proof of the non-denumerability of the continuum does not inspire a certain sense of awe within you, then you clearly know very little of mathematics and are not qualified to address this subject on a forum as distinguished and august as Adequacy.org.

 
In the future, (5.00 / 1) (#9)
by tkatchev on Thu Dec 20th, 2001 at 11:25:42 PM PST
...when a pill against lazyness is invented, I'll write a comprehensive explanation of why formal math is a liberalist scam. (I have extensive documentation on the subject, though I seem to have lost it at the moment...)

Suffice to say that, yes indeed, formal math is a scam. It is unfounded, a liberalist faith. (Face it, do you have the grounding to prove the basics of linear algebra? Well, the horrible liberalist secret is that almost nobody does. It's the blind leading the blind into the gaping chasm of liberalism.)


--
Peace and much love...

 
How do you type it? (none / 0) (#4)
by First Incision on Thu Dec 20th, 2001 at 08:25:04 PM PST
Slave, while your post was somewhat useful, and has prevented me from possibly offending you with punctuation (even though I usually just write "not"), you have not given us the whole story.

I used to have an old DOS manual that gave me all the shortcut keys for the ASCII characters. But my memory is fading. I do remember

é = Alt+0233 (use the numbers on the NumPad)

but only because that character is required to spell "resumé" when I'm feeling pretentious.

I don't feel like manually typing out all those numbers. What is the shortcut for your "not" symbol?
_
_
Do you suffer from late-night hacking? Ask your doctor about Protonix.

Perhaps you haven't located the switch? (none / 0) (#6)
by RobotSlave on Thu Dec 20th, 2001 at 08:57:46 PM PST
There is a clearly marked (although small) switch for the negation symbol ("¬") on the console of my writing mechanism. It's right under a row of large, durable levers for more commonly used symbols.

The marking can be hard to see, as depending on one's posture, it can be obscured by the ampersand ("&") and semicolon (";") levers immediately above it. That's just on my machine, though-- I have seen models where one must detach part of the console to access a lower level of buttons and toggles for certain uncommon characters.

Does that help?


© 2002, RobotSlave. You may not reproduce this material, in whole or in part, without written permission of the owner.

 
On a completely unrelated note: (none / 0) (#7)
by RobotSlave on Thu Dec 20th, 2001 at 09:07:02 PM PST
I feel, inexplicably, a festive holiday mood coming on, and I find I rather like it.


© 2002, RobotSlave. You may not reproduce this material, in whole or in part, without written permission of the owner.

 
you must mean... (none / 0) (#8)
by em on Thu Dec 20th, 2001 at 09:17:18 PM PST

\begin{equation*}
  (a \to b) \leftrightarrow (\neg b \to \neg a)
\end{equation*}
--em
Associate Editor, Adequacy.org

jsm, where are you? (none / 0) (#10)
by ausduck on Fri Dec 21st, 2001 at 12:07:13 AM PST
See here.

I hate TeX more than jsm does. (none / 0) (#12)
by em on Fri Dec 21st, 2001 at 12:28:09 PM PST
Because I know it, and have been editor for books done in TeX.
--em
Associate Editor, Adequacy.org

 
I feel nervous. (none / 0) (#11)
by RobotSlave on Fri Dec 21st, 2001 at 12:30:50 AM PST
According to descriptions I have read, this formulation you use bears many of the hallmarks of a "hacker" computer language.

I know, of course, that an adequacy editor would never use such a thing, so I will assume this must be some new notation that has been introduced since I allowed my subscriptions to the mathematical journals to lapse.


© 2002, RobotSlave. You may not reproduce this material, in whole or in part, without written permission of the owner.

 
Proper use for ~ (none / 0) (#13)
by legolas on Fri Dec 21st, 2001 at 06:29:43 PM PST
In the mathematical context, one possible use for ~ is to represent "approximately equal to". Now, I am aware that it is properly drawn as an =, either with one or more of the lines in a curvy, tilde shape, or as an equal sign with a curvy line over it. Now, without a proper font (such as Terminal, character 247), reproducing this character is not possible. Therefore, I would think that, barring using another font or an image, ~ would be an appropriate approximation for "approximately" or "approximately equal to".

-legolas


 
I could have sworn (none / 0) (#14)
by Lint on Wed Dec 26th, 2001 at 04:34:04 AM PST
that ~ is the negation symbol used in symbolic logic (as seen in a few simple arguments).

I believe most of those who solve problems of logic such as the above still rely on the tilde rather than the "¬" negation symbol. Perhaps they are uninformed of the advances in typesetting? My philosophy prof never did seem to get out much, now that I think about it...

Anyway, maybe that's what those poor, misguided tilde users were thinking of when using negation in argument. I have no idea where the "!" comes in. Regardless, thanks for clearing this up.


Your denial is beneath you, and thanks to the use of hallucinogenic drugs, I see through you. Bill Hicks

 
In re: Ars Matematica (none / 0) (#15)
by Orinoco on Mon Feb 4th, 2002 at 08:18:15 AM PST
I think this is an appropriate time for me to say that mathematics provides us with the answer to the timeless question first posed by Mr. Rodney King of Los Angeles, California. Mr. King's question was, as you recall: "Can't we all just get along, Goddamn it?"

The answer to which, echoing through an empty (null)set, is a tentative and whispered "No, Rodney."

And now on to more pressing matters, and specifically, who will help me with this problem:

a = b
multiply both sides by a gives
a2 = ab
add a2 - 2ab to each side gives
a2 + a2 - 2 ab = ab + a2 - 2ab
simplify to
2(a2 - ab) = a2 - ab
now divide both sides by a2 - ab gives:
2 = 1 !

...and so on and so on, all over the table like a madwoman's breakfast.


 

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