h a l f b a k e r yPoint of hors d'oevre
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As most half-bakers no doubt are aware, placing an exclamation point (!) after a positive integer n signifies the factorial operator n!=n(n-1)(n-2)...1, meaning that all postive integers less than or equal to the given number should be multiplied together to arrive at a solution. For instance,
1!=1
2!=(2)(1)=2
3!=(3)(2)(1)=6
4!=(4)(3)(2)(1)=24
and so on.
The arithmetic is really pretty straightforward -- but inexplicably, print and internet advertisers in particular appear to have fallen away from proper mathematical usage when financial matters are involved. I can't tell you the number of times I've been shocked (shocked!) at a coupon or advertisement brazenly promising to "SAVE $5!", while clearly having no intention of coming across with the actual sum depicted ($5!, or $120).
It is time that they pay for their enthusiasm.
Should you be so fortunate as to receive a coupon, spam email, or fake promotional check with any amount of money followed by a !, immediately present yourself at corporate headquarters with legal and mathematical representation and demand the full value to which you are entitled. The actual savings due on a coupon for $10! would come to just over 3.6 million dollars, while a sweepstakes offer such as "Win $50!" could result in an arbitrarily large, effectively infinite cash settlement.
There are a few caveats: Frustratingly, multifactorials such as n!!! increase somewhat more slowly than simple factorials n! for all values of n, giving particularly obnoxious offenders ("in less than 5 minutes, you can make $1000!!!!!!") a very slight reprieve. A case could be made that currency units distribute within the expression; thus a ($3)! coupon might only be redeemable in cubic dollars -- but I feel sure the parentheses would have to be expressly included in the promotional materials for that to be true. And for reasons I'm not totally clear on, zero factorial is defined as being equal to 1. So a credit agreement where "Your first month's payment is $0!" would actually go into default if you neglected to send in the $1 check.
All kinds of written communication could benefit from a more literal appreciation of this overlooked operator.
If after having won a $20! cash giveaway, lawyers for the advertising firm contact you with an offer less than the gross national product of Brazil, simply respond with the following message:
"I'll get back to you in several days -- I'm not sure how many, but it definitely will be less than 10!"
Factorial Tutorial
http://en.wikipedia.org/wiki/Factorial
Plaintiff's Exhibit A, may it please the Court. [dryman, Oct 04 2004, last modified Oct 21 2004]
Behold!
http://www.newdream...ld/numbers/fact.htm
[po, Oct 04 2004, last modified Oct 21 2004]
superfactorial
http://mathworld.wo...Superfactorial.html
[yabba do yabba dabba, Oct 04 2004, last modified Oct 21 2004]
Wikipedia on the Billion
http://en.wikipedia.org/wiki/Billion
1,000,000,000,000 [cFish, Oct 04 2004, last modified Oct 21 2004]
125! years of automobiles
https://www.faceboo...0.340071.6604386669
Did you know that the first motor-car was built and run before this universe began? [pocmloc, Jun 17 2021]
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Annotation:
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Top Quality!. In this world of litigation we should stand up to people who deliberately mis-sell. I can't believe that I missed this. |
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I predict that shortly this will become a top 10! idea |
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I predict you are wrong! !! |
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Well, I'm not going to bet you 20! |
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Thanks for the croissant it's delicious! I am now trying to work out a way to use trigonometry to sue the manufacturer of a tan-colored cot. |
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Now that is just a bad joke, dryman!
OH!SAH!COAT! |
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Welcome to the bakery, dryman. (WTAGIPBAN) |
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What a fantastically obscure and pointless idea. + |
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+ for math humour, a genre often overlooked. |
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+ Excellent. Re the [dryman] lawsuit, why not just cosh him over the exponent till he's powerless? |
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Nah, that would be a sin.. ;-) |
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// And for reasons I'm not totally clear on, zero factorial is defined as being equal to 1. // |
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Convenience. (These are mathematicians we're talking about - what other reason could there be?) |
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Nice. Especially the consideration
of 0!
[Reminds me of my
favourite promotional text which I
saw in a newspaper ad: "Buy 3 for
the price of 4 and get the 4th one
absolutely free!!!"] |
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I think that 0! = 1 comes from the patern that n! / n = (n-1)! , thus substituting 1 for n gives 1!/1 = 0!
Sorry slightly off topic... |
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Let's get algebraic.
What is x! ?
better still, what about lexicographic factorials?
How does dryman interpret a word followed by an exclamation mark?
Does dryman! become (dryma)(drym)(dry)(dr)(d) ?
Or do we work back through the dictionary, and get a string like.....
zenonian! = (zenith)(zenick)(zendic)........(a) ? |
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according to my calculator, dryman is approximately at 4.3622! |
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I tried a similar thing at an office supply store. They had folders on sale for .05¢ I tried to point out that that meant I could buy twenty folders for a penny, but the clerk wasn't smart enough to figure it out. |
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On a similar note, never go on any diet that promises "lose 10-20 pounds" -- you'll end up gaining weight. |
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Very good. Sadly, the highest number of positive votes I can give you is 0! |
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Misuse of the word "literally" is
always funny, and very common -
compare the fairly ordinary
metaphor "he exploded with rage"
with "he literally exploded with
rage".
([cFish] -
interestingly, your formula n!/n =
(n-1)! with n=0 implies that 1/0 =
(-1)!, or (-1)! is infinite) |
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I always thought it was literarily exploded with rage. |
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Rage, rage against the dying of the light. |
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You get +!... how much is that in croissants? |
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po, looks like I should have bet you that 20! |
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jutta -- how often does a first idea get this kind of reception? |
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[ydyd] Yes, I realized this and removed my anno. But shame on you for trusting your calculator. It can be easily found through logic. 1/x as x --> 0 from the right tends toward infinity. 1/x as x --> 0 from the left tends toward negative infinity. |
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Are you kidding me? What's anything divided zero times? It doesn't make any sense. Lim x--> 0 from both sides have to match. |
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Oh gosh n' golly, I may have just made us even richer.. |
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Looking toward the bottom of my link, it seems that the "superfactorial" of n is denoted n$. Now if you can find a coupon for an amount of money with vertical symmetry (say, $8), then what a simple matter to turn it upside down.. and solve the expression 8$ to see how much you've saved. |
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I don't actually know that much about math, but it seems to me from the wikipedia that what you would do is raise 8! to the (8!)th power, then raise that solution to the (8!)th power.. and do this a total of 8! times. Is this correct? Now *that* is a blisteringly, mind-meltingly large number. And it applies to every $8, $11, (or even better, $66) coupon on the planet. Advertisers -- beware! |
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Given that 1$ = 1! = 1, and
2$ = 2!^(2!) = 4, |
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I conclude that superfactorials are just the same thing as squares. |
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3! ^ 3! = 6 ^ 6 = 46,656, but I'm not so sure that's 3$.
Check the link--it looks like there's 2 different ways to do them. |
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3$ = 6^6^6^6^6^6 = good luck., or 3$ = 3! * 2! * 1! = 12 |
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In the first case: given that 3$ has well over 10e10 digits [rough mental calculation, might be a bit off], I think it'd be safe to assume there are very few places that'd give change for your voucher... |
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PS. that's 10 with 10 zeros after it, I'm thinking that'll be thousand millions for us UK speakers and billions for those state-side, and that's only the number of digits. |
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you guys say a thousand million? |
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Yep, a Thousand Million is 10^9, and a Billion is 10^12... I've added alink to Wikipedia that talks about it.. |
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I'd pay good money to see someone literally explode with rage. |
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// I think that 0! = 1 comes from the patern that n! / n = (n-1)! , thus substituting 1 for n gives 1!/1 = 0! Sorry slightly off topic...// |
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if 0! was found to be equal to zero early on there would be no need to define it as such... 0! is defined as zero because the factorial was first used to find the number of orders a set of n objects could be placed into, eg. {1, 2} could be ordered alternatively only as {2,1}... 2! = 2... since a set of zero objects can only be placed into 1 order(s) 0! was defined as 1... Later this definiton was found mathematically when the factorial was proven to be equal to the Gamma function... |
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It's intresting that the equality you described seams to work well even for negative numbers (I haven't checked them all but I've just glanced at a few tables) |
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I absolutely love this and think we should all try to take advantage of this. [+] |
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I will definitely use this! |
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Now this is just brilliant. I'm tempted to write to any company I see using this from now on... |
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If you applied this concept to the ads that say "you are our 1,000,000th visitor!" you would actually be aproximately their (8.26*10^5565708)th visitor. |
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//If you applied this concept to the ads that say "you are our 1,000,000th visitor!" you would actually be aproximately their (8.26*10^5565708)th visitor.//
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Would it not need to say "You are our 1,000,000! th visitor" for this to apply? |
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Is that The Pope, [monojohnny]? |
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I'm digging it. Our society is growing numb to the abuses of advertisers. Everything is blown out of proportion to get your attention. This would be a great way to both stop that and to encourage public numeracy. |
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I was trying to figure out how to squeeze Oklahoma!
into this idea. Perhaps inventing a series of
musicals called Alabama!, Alaska!, Arizona!, .. and
so on until Wyoming! And figuring out what the
product of a series of musicals might actually sound
like. It could be a big hit. |
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The number of positive votes I'm going to give this idea is
1! |
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