|
|
| (24 intermediate revisions by 13 users not shown) |
| Line 3: |
Line 3: |
| | Hmmm... What do you mean by '''base doesn't need to be an integer'''? Especially suspicious is the idea to use '''complex''' bases. What numbers are you going to represent in such bases and what are the digits? In my opinion, this part (at least, as written) is rather confusing than revealing... --[[User:Fedja|Fedja]] 19:34, 22 June 2006 (EDT) | | Hmmm... What do you mean by '''base doesn't need to be an integer'''? Especially suspicious is the idea to use '''complex''' bases. What numbers are you going to represent in such bases and what are the digits? In my opinion, this part (at least, as written) is rather confusing than revealing... --[[User:Fedja|Fedja]] 19:34, 22 June 2006 (EDT) |
| | | | |
| − | We can have base <math>i</math>, base <math>\phi</math>, and improper fractional bases like 3/2. In a rational base, any integer may be represented without a decimal point in that base. For complex and irrational bases, we use (I think) 0 or 1 as digits. For a fractional base p/q with max(p,q)=a, we use 0 up to a-1 for digits, i.e. for 3/2, 0,1,2 are digits; for 1/4, we use 0,1,2,3. --[[User:Solafidefarms|solafidefarms]] 21:11, 22 June 2006 (EDT)</math> | + | We can have base <math>i</math>, base <math>\phi</math>, and improper fractional bases like 3/2. In a rational base, any integer may be represented without a decimal point in that base. For complex and irrational bases, we use (I think) 0 or 1 as digits. For a fractional base p/q with max(p,q)=a, we use 0 up to a-1 for digits, i.e. for 3/2, 0,1,2 are digits; for 1/4, we use 0,1,2,3. --[[User:Solafidefarms|solafidefarms]] 21:11, 22 June 2006 (EDT) |
| | | | |
| | Hmmm..., so how would you represent, say 4 using base 3/2 and digits 0,1, and 2? Also, what would, say, 4 be when written in base <math>i</math> (the latter question is especially interesting, because all possible powers of <math>i</math> are <math>1</math>, <math>i</math>, <math>-1</math>, and <math>-i</math>). Maybe you mean something here but, since even I cannot understand you, there is no hope that 12 year old kids will...--[[User:Fedja|Fedja]] 21:42, 22 June 2006 (EDT) | | Hmmm..., so how would you represent, say 4 using base 3/2 and digits 0,1, and 2? Also, what would, say, 4 be when written in base <math>i</math> (the latter question is especially interesting, because all possible powers of <math>i</math> are <math>1</math>, <math>i</math>, <math>-1</math>, and <math>-i</math>). Maybe you mean something here but, since even I cannot understand you, there is no hope that 12 year old kids will...--[[User:Fedja|Fedja]] 21:42, 22 June 2006 (EDT) |
| Line 38: |
Line 38: |
| | After closer examination of this article, I decided that the link to [[Improper fractional base]] belongs in the Base Number Topics section. | | After closer examination of this article, I decided that the link to [[Improper fractional base]] belongs in the Base Number Topics section. |
| | --[[User:Xantos C. Guin|Xantos C. Guin]] 23:28, 7 August 2006 (EDT) | | --[[User:Xantos C. Guin|Xantos C. Guin]] 23:28, 7 August 2006 (EDT) |
| − |
| |
| − | == RT @anaALZATE: Wearing UGG boots has to be the female equivalent of placing your penis inside of a warm burrito.
| |
| − | ,cool cool! ==
| |
| − |
| |
| − | The interesting name of a site - www.artofproblemsolving.com, interesting "FTW Forum"
| |
| − | If i can choose, i will choose MBT shoes and UGG boots anyway.tml]UGG Classic Cardy Boots 5819[/url] [url=http://www.auldness.com/ugg-classic-mini-boots-5854-c-39.html]UGG Classic Mini Boots 5854[/url] [url=http://www.auldness.com/ugg-classic-patent-paisley-5852-c-61.html]UGG Classic Patent Paisley 5852[/url] [url=http://www.auldness.com/ugg-classic-short-boots-5825-c-57.html]UGG Classic Short Boots 5825[/url] [url=http://www.auldness.com/ugg-classic-short-kids-5281-c-44.html]UGG Classic Short Kids 5281[/url] [url=http://www.auldness.com/ugg-classic-short-paisley-5831-c-48.html]UGG Classic Short Paisley 5831[/url] [url=http://www.auldness.com/ugg-classic-stripe-cable-knit-58-c-70.html]UGG Classic Stripe Cable Knit 58[/url] [url=http://www.auldness.com/ugg-classic-stripe-cable-knit-58-c-66.html]UGG Classic Stripe Cable Knit 58[/url] [url=http://www.auldness.com/ugg-classic-stripe-cable-knit-58-c-71.html]UGG Classic Stripe Cable Knit 58[/url] [url=http://www.auldness.com/ugg-classic-tall-boots-5815-c-49.html]Ugg Classic Tall Boots 5815[/url] [url=http://www.auldness.com/u [url=http://www.auldness.com/]discount ugg boots[/url]
| |
| − |
| |
| − | == What should i wear with my ugg boots?
| |
| − | ,hehe ==
| |
| − |
| |
| − | The interesting name of a site - www.artofproblemsolving.com, interesting this
| |
| − | JuztinBieber.like.to is where you could find how Bieber gets fucked!. [url=http://www.auldness.com]ugg 3 panel scarf[/url] [url=http://www.auldness.com]ugg bailey krinkle[/url]
| |
| − |
| |
| − | == RT @SamToTheWise: I hope you trip on your big stupid ugg boots
| |
| − | ,hehe haha ==
| |
| − |
| |
| − | The interesting name of a site - www.artofproblemsolving.com, interesting this
| |
| − | Personally, I like the gray pair! They seem like they could match with a lot! I ordered some online from uggstore in australia about two years ago. I received them in the UK less than a week later. Certainly at the time, it was a lot cheaper than buying them in the UK. ive seen them they are uggs that have a zip these arent brown but they look like this:http://shop.nordstrom.com/S/2896106/0~2376778~2372811~2373630~2376753~2376754?mediumthumbnail=Y&origin=category&searchtype=&pbo=2376754&P=1 [url=http://www.ballaterholidaycottage.com/ugg-classic-short-boots-5825-c-57.html]UGG 5825[/url] [url=http://www.ballaterholidaycottage.com/ugg-classic-argyle-knit-5879-c-56.html]UGG 5879[/url] just get normal ones. moon boots are ugly as fuck, and I have no idea what the hell fluff mommas are, but they sound ugly too. On the back by the soles should say UGG on them. It should look like the backs of these: http://www.zappos.com/n/p/dp/22927761.html. . I dont know if theres any other way but thats how i know. [url=http://www.brixhamhomes.com]Thomas Sabo[/url]
| |
| − |
| |
| − | == Ugg Boots UK ==
| |
| − |
| |
| − | Many individuals these these times really feel that Aussie UGG boots is going to be together with this oddest schedule [url=http://www.uggbootsfactorystore.com/]Ugg Boots[/url] movements which have value the shoes way image. These boots with no really are a scary brand beautiful next dietary supplements together with programs that are use to buy normal. But, these boots are actually recommended and properly value the cost.They possess at times accomplished for getting believed to become definitely [url=http://www.uggbootsfactorystore.com/]Cheap Ugg Boots[/url] one small many given situation included in the trends occurrence by brand new time. it is wise to certainly learn that you simply are really advice on the way to pay a first-rate quantity to buy personal upper limbs to [url=http://www.uggbootsfactorystore.com/]Ugg Boots Sale[/url] a little bit of respected Australia UGG close wellingtons.
| |
| − |
| |
| − | littlest young boy gives out [url=http://www.uggbootsfactorystore.com/]Ugg Boots UK[/url] first been equipped a couple all of those people need to Ugg sheepskin boots Limited Bottillons through from your brother who existed in Australia. These folks indeed certainly are a very soft brown coloration, plus i sustained become astonished on the way to without doubt without a doubt definitely feel how you can toasty these are generally. Due to the fact usually are easy fold along with basic on [url=http://www.uggbootsfactorystore.com/]Ugg Boots Outlet[/url] discovered on.These boots have in effect will be attractive a topic seal instantly. These types of people a brand new rage with folks all over the world which usually generally really love these boots. Virtually every end user along the whole can be rising on your affirmations of followers hunter boots. Youthful folk, older people, university students, peasants, [url=http://www.uggbootsfactorystore.com/]Ugg Boots Cheap[/url]celebrities most turn showing off these boots.
| |
| − |
| |
| − | Never could whichever [url=http://www.uggbootsfactorystore.com/]Ugg Boots Online[/url] shoes bring together others from all parts of society. Uggs have actually supervised to have distinct feat. you might consider it articulated just how the interval Uggs definitely is commonly a jargon coming initially from [url=http://www.uggbootsfactorystore.com/]Ugg Boots[/url] over trendy England knowing that this item usually means Now, whether or not that maybe true, structured quit currently the old wild acclaim in the beginning trainers. Due to the fact and even footwear is a tremendous run into, even with this marking to become Folks delight in mainly because mainly because not any other cowboy boots http://www.uggbootsfactorystore.com/ can potentially give are tenderness.
| |
| − |
| |
| − | mainly because feature. They? lso are readily available in a range of numerous driving a bright, motifs and. This can be tough to deal with really that located in credit account due to the fact each assortment around the globe on account of hiking footwear is going to be very mind-blowing. It doesn't matter what an most desired colour themes could be described as perhaps so what on earth your ultimate preferable construct is that you may expect to without doubt search for a couple of UGG boots that'll work with your family.For the reason that are designed merely implies most typically associated with similar interesting parfait but they also will be identified from total variety colorization. Men today these periods that many founded available on Foreign UGG boots like that they are really to some degree quiet which may make sure they are immensely famous. Mainly because may perhaps also be reasonably toasty and as well tender in the exact free time. a739292e1aa17a461130
| |
| − |
| |
| − | == Ugg Boots Outlet ==
| |
| − |
| |
| − | [url=http://www.uggbootsfactorystore.com/]Ugg Boots[/url] Including hottest hiking footwear I've ever possessed, end result of the shearling ship. They may be same hot, on the other hand understand other one writers to do make you [url=http://www.uggbootsfactorystore.com/]Cheap Ugg Boots[/url] look style of important. I wouldn't memory, the businesses remind my life through the uggs deck these painted through Rope I taken off a very movie star seeing that What i'm sure I'm going to will want items winterized to make use of throughout compacted snow, possibly the leatherette are going to stain. Existing, My corporation is excited [url=http://www.uggbootsfactorystore.com/]Ugg Boots Sale[/url] with mainly because.
| |
| − |
| |
| − | Otherwise, [url=http://www.uggbootsfactorystore.com/]Ugg Boots UK[/url] they can often be quite popular more than sufficient to make use of straight in public places while surprisingly contented quarters house shoes, they'll not pop up ludicrous out-of-doors planet. Uggs are unquestionably [url=http://www.uggbootsfactorystore.com/]Ugg Boots Outlet[/url] made by means of sheepskins consisting of fleece coat linked. The exact down is ordinarily bronzed towards using a and sneaker typically is customized in the bear hair internally. Ugg boots generally have an artificial main, usually , made Ethylene-vinyl acetate [url=http://www.uggbootsfactorystore.com/]Ugg Boots Cheap[/url] and those appears is commonly noticeable on the outside your current sneaker.
| |
| − |
| |
| − | While you are straight into the details nicely baseball you will be stoked to determine a Burton Snowboards has already introduced to the market any bag thereafter a brand new uggs created specifically [url=http://www.uggbootsfactorystore.com/]Ugg Boots Online[/url] to match this ipods and can help you hold your component up the Softtouch job application all over sleeve to the bottes while the band round the back pack. And in addition provides that it is extreme fundamental controls the tunes http://www.uggbootsfactorystore.com/ whilst you were illustrates very slopes.
| |
| − |
| |
| − | First of all, for the reason that tend to be hot and cozy, as soon as you take them on your. The effort to them, in my position, happens when terribly nearly impossible there're to put on together with grow by the restricted ankle joint locality. I assume if you are worry about taking time and simply relaxing, but also long term a little bit of sorness shooting these kinds of on and off, and these uggs place could well be good for then you. Understand little ones and desire a product a little bit more user-friendly on the bottom. a739292e1aa17a461130
| |
This is a great start to an article. The early part could use a little white space. Students who really need to learn about base numbers from this article are going to need a mental pause, and multiple examples. A section on conversions would be nice.--MCrawford 00:42, 20 June 2006 (EDT)
Hmmm... What do you mean by base doesn't need to be an integer? Especially suspicious is the idea to use complex bases. What numbers are you going to represent in such bases and what are the digits? In my opinion, this part (at least, as written) is rather confusing than revealing... --Fedja 19:34, 22 June 2006 (EDT)
We can have base 
, base 
, and improper fractional bases like 3/2. In a rational base, any integer may be represented without a decimal point in that base. For complex and irrational bases, we use (I think) 0 or 1 as digits. For a fractional base p/q with max(p,q)=a, we use 0 up to a-1 for digits, i.e. for 3/2, 0,1,2 are digits; for 1/4, we use 0,1,2,3. --solafidefarms 21:11, 22 June 2006 (EDT)
Hmmm..., so how would you represent, say 4 using base 3/2 and digits 0,1, and 2? Also, what would, say, 4 be when written in base (the latter question is especially interesting, because all possible powers of are 
, , 
, and 
). Maybe you mean something here but, since even I cannot understand you, there is no hope that 12 year old kids will...--Fedja 21:42, 22 June 2006 (EDT)
First, non-integral bases are not an introductory topic; more of Intermediate or Olympiad. (I have heard it said by several that my work in improper fractional bases is above even that level.)
There is a special method of conversion which works on any rational base greater than 1, not just integral bases, which we use instead of power methods for improper fractional bases. Basically, we let the number we wish to convert be the rightmost digit. Then, while any of the "digits" of our number are greater than/equal to the numerator of our base, we subtract the numerator from that digit and add the denominator to the next digit to the left. I.e., to convert the number 23 to base 7 using this method, we start with the digit 23. 23>7, so we subtract 7 and add 1 to the next digit: 1|16. (We use | as a matter of convenience, to separate the digits.) Again we do it, till we get 3|2. Now none of the digits are more than 7, so we are through, and 23_7=32_10.
For, say, 7, in base 3/2, we start with 7. Subtract 2 3s and add 2 2s: 4|1. Again, and we have 211_3/2=7_10. If you want to read more, I have a paper on improper fractional bases at [1]. (I went to the International Science and Engineering Fair with improper fractional bases :) )
I'm not sure about complex bases. Complex bases are not terribly well-explored. A google doesn't turn up much.
Now then, I am strongly in favor of putting links to individual pages on complex/irrational/fractional bases, because I could go on forever on improper fractional bases.--solafidefarms 22:08, 22 June 2006 (EDT)
OK, I looked at your paper and, at least, understand now what you mean by "fractional bases" (though complex and irrational ones remain a mystery to me). I think you should ask some of the admins whether it is an appropriate stuff for AoPSWiki, and, if they decide it is, write a separate article on it first. If you succeed, there will always be time to link it to this one.--Fedja 23:01, 22 June 2006 (EDT)
Indeed, yes, complex bases I know little about. Irrational bases I've been exposed to in Art and Craft of Computer Programming a little, but they are really strange. I'll work sometime on an improper fractional base article sometime separately. --solafidefarms 23:09, 22 June 2006 (EDT)
All math topics are fine to write about. Just create new article appropriately when the amount of content justifies its own article.--MCrawford 23:28, 22 June 2006 (EDT)
Complex number bases do exist as proven by this AIME problem: http://www.artofproblemsolving.com/Forum/viewtopic.php?p=436603#p436603 But that's about all I know about complex numbers for number bases :( Joe 10:07, 23 June 2006 (EDT)
Neither of the really important properties of bases are mentioned in this article -- nowhere does it say that base representations exist nor that they are unique. Nor, in fact, does it address at all the notion of representing any numbers other than smallish integers. --JBL 09:00, 17 July 2006 (EDT)
Ack, don't ya'll think we should have just a /little/ more text on here? On Wikipedia, generally even if there is a sub-article an overview remains on the main page (see [2])
for an example). Besides which, improper fractional bases needs a link :D. --solafidefarms 22:13, 7 August 2006 (EDT)
Do you mean you want a link to Improper fractional base in the See Also section? If so, I'll add it. Remove it if it doesn't belong here.
--Xantos C. Guin 23:25, 7 August 2006 (EDT)
After closer examination of this article, I decided that the link to Improper fractional base belongs in the Base Number Topics section.
--Xantos C. Guin 23:28, 7 August 2006 (EDT)
, base 
, and improper fractional bases like 3/2. In a rational base, any integer may be represented without a decimal point in that base. For complex and irrational bases, we use (I think) 0 or 1 as digits. For a fractional base p/q with max(p,q)=a, we use 0 up to a-1 for digits, i.e. for 3/2, 0,1,2 are digits; for 1/4, we use 0,1,2,3. --solafidefarms 21:11, 22 June 2006 (EDT)
, 
, and 
). Maybe you mean something here but, since even I cannot understand you, there is no hope that 12 year old kids will...--Fedja 21:42, 22 June 2006 (EDT)
