mathdreams

There is a mathematical joke that people like to send around sometimes of a proof showing all numbers to be equal:

Theorem: All numbers are equal.

Proof: Choose arbitrary a and b, and let t = a + b. Then

1.) a + b = t

2.) (a + b)(a - b) = t(a - b)

3.) a^2 - b^2 = ta - tb

4.) a^2 - ta = b^2 - tb

5.) a^2 - ta + (t^2)/4 = b^2 - tb + (t^2)/4

6.) (a - t/2)^2 = (b - t/2)^2

7.) a - t/2 = b - t/2

8.) a = b

This proof falls when you go from step 6 to 7 because the +/- is not accounted for when taking the square root.

In this proof I think we're assuming we're working in either R or Z, but what if we confine it to N, the set of natural numbers.

Then would we not have to worry about the square root having +/- values? But then, if a=b, then a-b=0, and 0 is not an element of N, so if we made it a more rigorous proof by going backwards (because right now, only implications really exist between each step, not equivalencies), would it then fall apart because of step 2?

I work at a Hallmark store and we sell Webkinz, Signature Webkinz, Junior Webkinz, Kinz Clips, and Zumbuddies. None of the Webkinz stuff was around when we were younger and so none of us really know what the different things do. We know that all of them have these special codes and you can go online and it's like a virtual world and stuff. However, we have no idea what the difference between these different types are. We had a customer come in today and ask us why the Signature Webkinz is $29.99 and the regular Webkinz is $14.99. We told them that part of it is probably because the Signatures are a little bigger and nicer quality stuffed animal, and there are less of them available than the regular Webkinz, but other than that we don't really know. The woman asked if the Signatures have anything special or extra for the online stuff, we had absolutely no idea. I tried looking on their website (www.webkinz.com) but it didn't even say anything about Signature Webkinz anywhere on the website.

I would greatly appreciate it if someone could really explain to me what each of these things is really all about. It would really help all of us at the store be able to better explain to customers (especially adults buying them for gifts for kids) what these things are all about. Customers sometimes get frustrated when you don't really know all that much about a product that you're trying to sell.

Also, I think it would be interesting to know for my own personal knowledge; when I was little Giga Pets were the big thing and those were way simpler and less complicated than all of this Webkinz stuff.

Thanks So Much!

Ok. So I was in an accident this last Friday and I want to make sure that when my car is appraised that I'm actually getting a fair price. I'm hoping that by asking this question I could get some answers from either someone who currently sells cars at a car lot of some sort, or someone who used to sell cars at a car lot, or someone who just knows a LOT about this stuff, so here's everything I would consider pertinent to the price of the car if I would've sold it myself (I've looked at a lot of used cars private party before):

1998 Maroon (Dark Red) Camry LE, 4D (not the V6)

It has about 102,000miles on it, and 75% of the last 13,000miles were highway (driving from Spokane, WA to Seattle, WA)

It came with all of the standard factory options, it's additional options are:

Gold package (it has the gold emblems instead of the silver)

Fog Lights

Moon roof that slides and tilts (and has sun/wind reflector cover)

Alloy Wheels

Mud Flaps

The upgraded entertainment package which includes AM/FM radio, cassette, Single CD player, 6 speakers (I believe 4 are regular and 2 are tweeters, but it's all manufacture Toyota stuff)

Toyota VIP Security System (I have the beeper for it)

Other additional information I would include would be that I have 4 Yokohama iG20 snow tires for it which have only had one season and the current tires are all weather and still in good condition. I have ALL the owner's manuals (the owner manual, supp owner manual part 1&2, the VIP owner manual). I also have a Haynes Repair Manual for it. The spare tire is still intact. Before I bought it in Feb 2008, the car had only had one owner (ie I'm the second owner) and it has a clean title, all of which can be verified by carfax. I have kept a record of all the oil changes it has had since I bought it in Feb 08, it had 85,456 when I bought it, I changed the oil at 90,989 in Aug 08, I changed it at 94,917 in Jan 09, I changed it at 98,895 on May 15, 09.

Also, on May 15, 2009, I had a TON of tune-up/service work done. The spark plugs were replaced (iridium plug, dual tip), the fuel filter was replaced, the air filter was replaced, some sort of wires were replaced, the invoice sheet says Tailor Mag Cor Wires, it has a Minor tune up of Electronic Ignition, the transmission fluid was replaced, it says Belt ALT which I would assume means the Alternator belt was replaced?, it says Belt STG which I would assume means the steering belt was replaced?, the timing belt was replaced, the engine front oil seals were replaced which I believe includes the camshaft and crankshaft oil seals, the water pump was replaced, and the antifreeze/coolant was changed. I have the invoice for all of this and the receipt showing I paid for it; the total ended up being $1053.26.

As far as it's interior and exterior condition, I would obviously shampoo the carpets and clean everything if i was selling it, but I'm not sure if the appraiser will take that into consideration, the drivers side carpet has a fair amount of dirt stains due to the fact that the car was missing the floor mats when I bought it and I spend my winters in muddy, sandy, snowing Spokane, WA. However I have no idea how much of that would come out. Other than that the interior is in good condition for it's age. The exterior shows some minor wear and tear, the driver door was keyed but it's not too bad, very light and superficial, I have one fairly bad scrape with a dent, someone at the University obviously scraped me while parking, however, I would estimate no more than $500 repair, other than that the only other exterior issues are two small dings in the windshield and some teeny, tiny paint dings on the front and hood area just from lots of highway driving and driving on sanded roads. Speaking of sanded and salted roads, while the roads were salty and sandy here in Spokane this last winter I took my car in to be washed, with an undercarriage wash about every other week. Oh, I also have a set of regular tire chains with some rust on them, but they're still good, only used them this last season, oh, and I would include a set of jumper cables.

I have 1 clicker for the alarm system and I believe I have at least 4 sets of keys to the car. In my humble and biased opinion, the car is worth at LEAST $7,000, I mean, I paid 6,030 for it back in Feb 08, but that's because I had cash on hand and the guy selling from a small used car lot it thought it was a CE, not an LE (which it is, a Toyota dealership verified based on the VIN) and the guy didn't realize it had only had one owner. They had their listing price as $7,995.

Truly, I want my car to be fixed and not declared a total loss, but that's going to be difficult considering both the airbags deployed. However, it seems that the only non-structural damage (ie the front bumper destroyed, the hood slightly crumpled) the only damage they think is sustained is a broken windshield washer reservoir. So, if ANYONE can help me figure out ho

I have a philosophy paper due in about 8hrs. I'm comparing Plato's views of education reflected in the Republic, with St. Augustine's views on education reflected in Confessions. I have got all of the stuff about Plato down, but I need to figure out what Augustine's views on education are. I'm looking for things such as how he thinks education should be conducted/structured and what should be studied. If someone could just tell me what parts of what books to find this information in that would be REALLY AWESOME!!!!!

The countdown clock is ticking, it's 2:17am where I am and I have to be in math class at 9am, which is when I have to be done with the paper!

Thank you so much for all of your help!

I have tried to research the types of dreams I have to really no avail. Essentially, if I am doing homework right before bed, I obsess about doing that homework in my sleep. I'm a math major, so for math people, basically, I have woke up and realized that I was dreaming about how to solve one of those circular seem like they're never going to end integrals and I can't figure out the answer. In my dreams I have tried to come up with theorems and proofs for things, even after I wake up, when I try to go back to sleep it starts again right where I left off and I never actually solve anything, at least I can't remember an answer when I wake up. Besides just math, I have also obsessed about literature, I've found myself trying to write papers in my dreams, etc. I also have dreams where I just visualize repetitive patterns. It drives me nuts because I wake up with severe physical symptoms of anxiety and I'm exhausted. Does anyone suffer from a similar problem?