.999 repeating does not equal 1

Scott Wilhelm nerd-sniped me with this video that claims infinity equals -1

The method used in the video is being basically the same method used in the false proof that .999 repeating = 1.

I believe that both of those proofs are wrong. The problem is that they are engaging in mathematical legerdemain and using an infinite series as a real number. But I don't believe it is mathematically possible to use infinite series as a real number. You can't multiply it by anything. It is infinite. You end up with terms that cannot be mixed, like a blue mile or a red 65 miles per hour. It just doesn't make sense or describe anything real.

This is here is some fucking crazy calculus, but I think it is basically saying you cannot treat an infinite series as a sum, which is what the .999.. = 1 and the infinity video are trying to do. See the part beginning with:

Before we move on to a different topic let’s discuss multiplication of series briefly.

It says that you cannot treat multiplying a series as just multiplying the constant terms, you have to distribute each term into each other and then combine them, which is literally impossible when dealing with an infinite series. The only way to do it is to represent it with notation (which is another infinite series), but you cannot derive a real number out of it. And that is the key. An infinite series is not a sequence of numbers. See the concluding two paragraphs:

We’ll leave this section with an important warning about terminology. Don’t get sequences and series confused! A sequence is a list of numbers written in a specific order while an infinite series is a limit of a sequence of finite series and hence, if it exists will be a single value.

So, once again, a sequence is a list of numbers while a series is a single number, provided it makes sense to even compute the series. Students will often confuse the two and try to use facts pertaining to one on the other. However, since they are different beasts this just won’t work. There will be problems where we are using both sequences and series so we’ll always have to remember that they are different.

In that the infinity video, the speaker is giving us an infinite series and then claiming that is identical to a sequence of digits that can be cancelled out using another sequence. But you can't do that. You can't compare an infinite series to a sequence in that way. It's an abuse of terms.

An infinite series is a single number, provided it makes sense to even compute the series. And in that case the computation of the series is a number, but that is not the same thing as saying the series itself is the number. That's the same as how a fully grown apple seed is a tree, but an apple seed itself is not a tree.

If you want to perform mathematics using series you must use only series. In that case you are using notation so you would use .999.. and never resolve it to a real number. If you have an infinite series and you want to use it with real numbers you must take the limit of it, which is more crazy calculus but as I understand it it is a way to find the real number to which the series gets the closest (if any) with infinitely diminishing margin of error. In the case of .999.. that is in fact 1, because there is no real number closer to .999.. than 1.

BUT, in this case we aren't saying that .999.. equals 1, we are saying that the limit of .999.. is equivalent to one. Those are not the same statements.

LONG STORY SHORT:

You can say that 1 = 1 or that .999 to infinity = .999 to infinity, but you cannot say that .999 to infinity equals 1. It is exactly like this:

An apple equals a fruit.
An orange equals a fruit.
If you cancel out the fruit term, you get an apple equals an orange.

But you can't compare apples to oranges!

The infinity video I believe both has the method wrong and the conclusion wrong. Infinity is not equal to -1, because the limit of infinity is not -1.

The .999 repeating equals 1 has the method wrong, because you can't perform sequential number calculations on an infinite series, and the conclusion is syntactically wrong. It's the limit of .999.. that is equal to 1.

I know some posters on Dark Taco are much better trained math wizards than I. What say you?

The House Rental Industry Sucks

A multitude of property management companies carve up the rental space into countless little overlapping fiefdoms making it difficult to rent a house and wasting home owners money. This is generally bad for everyone involved and needs to stop.

Every town/suburb I've looked for housing in, has multitudes of rental/property management agencies. So if you want to rent a particular house you have to deal with one group of incompetent twits. If you instead want to rent the house across the street you get to deal with a completely different set of inept knuckle draggers.

Most property management offices will require you to fill out an application with all kinds of basic information and pay for a credit check. Not that difficult, but each and every place you look at will have a different application an yet another $35 credit check. To add insult to injury they will probably require that you fax them your application if you cannot make it to their office durring business hours.

This is ridiculous! For one thing, "office hours" are probably the standard 9-5, which doesn't make a lick of sense. If I have a steady job to pay rent, you might suppose I would be busy from 9-5, probably.  So I can't make it in durring office hours, I'll just fax that application in. Oh wait, the fax didn't go through, the line was busy, the machine at Kinkos was labeled wrong and I fed my application through upside down so your machine just spit out 3 blank pages, the application came through but my signature was cut off, what else could go wrong. Fax machines are and have always been a terrible idea.

This whole conundrum could be solved by a secure web form, and a centralized credit check. I would do one credit check and it would be good for say 3 months, durring which time I could just send my results electronically with my on-line application to any agency. Wouldn't that be nice?

Earlier I say this whole pile of last weeks dinner wastes home owners money, let me justify that claim. When a home owner wants to rent out her house but doesn't want all the hassle of actually being a landlord, she can turn to a property management company to do the dirty work for her.  Property management agencies typically get paid monthy  for maintenance and get a finders feed based of the first months rent when a new tenant moves in.

This means the motivation is all wrong, the property management company is motivated not to get a new tenant as soon as possible but instead with as little work on their part as possible. Which ads up to the property staying vacant longer and the potential renter gets lousy service. The owner is out months of rent and the renter if frustrated to the point of accepting whatever they can find, instead of exactly what they want.

If we could change the industry so that the agencies would be financially motivated by helping the renter find a place rather than doing as little work as possible, houses would rent faster and renters would be happier.

This has been a rant by The Angry Hippy thanks fore reading.

Solar Reigns in the Black Forest

One thing I keep running into while visiting southern Germay is a perponderance of alternative energy. Windmills and solar panels are in every skyline. Even though you cannot see the sun.

Take this barn for an example. I took this picture in a sleepy little wine producing village that is over a thousand years old. By my best guess the barn in the picture is over 500 years old, and covering almost its entire southern roof are two huge solar arrays.

To put this amazing blending of ancient and modern in perspective, I haven't seen the sun in weeks, its not like we are in sunny California where solar collectors would work year round.

Anyway, just wanted to share this amazing observation bulidings older than the country I live in with state of the art technology on the roofs. Lets get it together and follow Germany's example. If we were willing to put solar pannels on every available surface like they are, we would be a lot closer to energy independance.

auf wiedersehen

Bad Science Journalism

Seriously, does the bad even need to be up there anymore, or has Science Journalism become synonymous with Bad for other people as well. I was reading this article from reuters about Solving the Anti-Matter Mystery. There are some problems with this post in my opinion.
First off, they don't mention what the Anti-Matter mystery is really, maybe they are hiding underneath the sink. They also confuse it with solar power, dark energy and dark matter. They also seem to be convinced that we don't know what it's made of, perhaps that was the mystery. Also mysteriously absent was the fact that anti-particles have been being stored at accelerator facilities for years, and that this was significant because they were neutral atoms being stored. I guess they mentioned the word neutral in the article somewhere else, it's good enough right?
Maybe I'm being too critical, but it seems like you could quickly modify this article to be about nearly anything by just changing some nouns.

Cutout Cake (Image Overload)

This week in Dessert Theatre, I concocted a special treat for my sister's birthday. I spent quite a bit of time planning, and though the cake wasn't perfect, it came out wonderfully in the end.


I pulled resources from bakebakebake, the LJ community, as always, and went to my two standby recipes. My sister asked for a white cake with vanilla frosting. When asked about colors, she said blue and green. My trusty white cake recipe from AllRecipes.com came to my side, heavily fused with Wilton's icing coloring. My basic vanilla buttercream recipe* - a rich, buttery and smooth frosting - did the trick of icing, also heavily infused with Wilton's coloring.


What is truly special about the cake is what I did to the inside, though:


I was inspired by this tutorial, which can also be found within the annals of bakebakebake.

But I made four separate cake recipes, and four batches of buttercream. What did I do with all the extra, you ask? Well, I'm so glad you asked...


Cake balls! Heavily inspired by many, many places, most notably Bakerella.

These were pretty delicious, and I found out that, per ounce, dark chocolate gets more coverage than milk or white chocolate, as it is thinner when melted.

All in all, I produced a 6" wide 7.5" tall cake, and 88 cake balls. For more photos, in progress shots, and images of my dirty kitchen, you can check out the Picasa album.

*I have no idea where I found this, but recipe as follows:
1 stick butter (1/2 cup), room temperature
1 tsp vanilla extract
2 cups powdered sugar
1 tbsp hot water
Beat until smooth and creamy
(If the butter is too cold, you'll get a spotty effect in the icing)

Cass Divine - A Web Comedy: Episode 0

Our proto-episode is live on Kickstarter!



We're still trying to drum up interest, so go check out some of the extra features we're hosting exclusively on Kickstarter!

Chocolate Chip Cookie Dough Cupcakes

Or, in other words: Mouthgasms*.

Tonight's Dessert Theatre starts like usual; I was going through the daily posts of bakebakebake, the LJ community I follow dedicated to baking, when someone posted this glorious recipe** - although, they forgot a couple things, like what temperature to bake them at, but it turned out alright in the end.


* 1 18 ounce package of cookie dough
* 24 cupcake liners
* about 1 1/2 cups chocolate chips, depending on your taste
* 1 18.25 ounces box of yellow cake mix
* 1 3.4 ounce box of vanilla instant pudding mix
* 1 cup whole milk
* 1 cup vegetable oil
* 4 large eggs
* 1 teaspoon pure vanilla extract

1. Preheat oven to 350 degrees.
2. Put the cake mix, pudding mix, milk, oil, eggs, and vanilla in your big mixing bowl.
3. Mix with an electric mixer until combined (2 minutes-ish) scraping down the sides again if needed. The batter should look well blended.
4. Stir in the chocolate chips.
5. Take a 1/4 cup measuring cup to scoop batter into each lined cupcake cup for a total of 24 cupcakes.
6. Push a frozen cookie dough chunk in the middle of each cupcake.
7. Bake the cupcakes until they are goldeny done – for about 20 to 25 minutes.

Cookie Dough Frosting

* 3 sticks unsalted butter, at room temperature
* ¾ cup light brown sugar, packed
* 3½ cups confectioners’ sugar
* 1 cup all-purpose flour
* ¾ tsp. salt
* 3 tbsp. milk
* 2½ tsp. vanilla extract

1. To make the frosting, beat together the butter and brown sugar in the bowl of a stand mixer fitted with the paddle attachment until creamy.
2. Mix in the confectioners’ sugar until smooth. Beat in the flour and salt. Mix in the milk and vanilla extract until smooth and well blended.
3. Frost the filled cupcakes as desired, sprinkling with mini chocolate chips and topping with mini chocolate chip cookies for decoration.

The frosting was rich, buttery, and sweet. The cupcakes were a hint salty, and moist, and the cookie dough on the inside - it was like a magical gift from the oven. Though the mini morsels did not stick to the frosting very well - I had to pat them in - they still enhanced the overall cupcake experience.

I'd say this was a success, and I encourage everyone to try these. The cupcakes themselves are simple doctored box mix type, so it's hard to mess it up. They are very rich, however, and you should probably limit yourself to one (and not eat dinner for the rest of the week) if you're considering calories.

*This is a portmanteau of mouth and orgasms, just in case anyone is not clear.
** The recipe (edited with the temperature after I mentioned it to her): http://www.lovintheoven.com/2010/06/chocolate-chip-cookie-dough-cupcakes.html

Cass Divine - A Web Comedy: Cass Divine on Kickstarter.com!

It's live! We've created a web series concept, assembled a team, and now we have a photomatic trailer on Kickstarter.com to drum up support for the project! Go check it out here: http://www.kickstarter.com/projects/roysteves/cass-divine-a-web-comedy

Synopsis:

Even supernatural economies have downturns. Over the past 2,000 years, the funding for experimental research in the mortal realm has been slashed again and again. Now, two supernatural beings are in desperate need of a perfect test subject, and this time the fate of all humanity is up for reconsideration.
Cass Divine is just a student. This makes her the perfect blank slate, the perfect test subject.

No harm is intended, but an experiment wouldn't be necessary if the results were foreseeable!

Once again, the best place to go to check out the project is where the grassroots effort is centered: http://www.kickstarter.com/projects/roysteves/cass-divine-a-web-comedy

However, as the youtube version is slightly higher quality, in full screen...

You can read more about the cast, crew, and project on the Cass Divine website, too!

So, what do you think?

Fixed aspect ratio bug work around for windows 7

Recently I ran into a problem using windows 7 where I could not get the nvidia driver to not scale the resolution on my monitor. This is primarily a problem when playing old video games that don't have wide screen modes. Since I didn't want to look at squat jedi, I researched a fix, but since it was hard to find I'll post it here as well:

Step 1: Put your screen resolution to a non-native mode in the nvidia control panel.
Step 2: Change the scaling option to "Do Not Scale" and hit apply.
Step 3: Verify that you are now looking at a non-scaled non-native screen.
Step 4: Put your screen resolution back to the native resolution.

That should just about do it. I had this setting hold through several restarts as well. Now, go enjoy your old video games, they miss you.

Divinity

No, no, not the mystical thing from being a higher power of some sort. Tonight in Dessert Theatre, we're discussing the dessert, divinity. Like a vanilla fudge, it is rich, melts in your mouth, and is very, very sweet.

It is also about 90% sugar.
And looks like clouds.

I lifted this recipe directly from about.com (I will not be copying the recipe, just click the link), but it turned out very well, and was very easy to follow. The hardest part I found was getting my thermometer to stay in the liquid syrup while it was boiling and not touch to the bottom or sides of the pot. In this endeavor, I ruined a hair clip, but it was well worth it.

Divinity originated sometime in the early 1900's, when corn syrup was first coming to public attention, and the companies that produced it were inventing recipes for its use, both in combination with and in replacement of granulated sugar. Divinity was one of these created recipes, and no one really knows there the name came from. It is speculated that when first tried, it was hailed as "divine."

Divinity is also a very temperamental sweet, as if it is too humid (above 50% or so), the divinity will not set, and will instead absorb the moisture in the air and become, well, a giant gooey mass of sugar.

Some small advice for ease of creating this: If making it alone, have a stand mixer. If all you have is an hand mixer, get a buddy to help. If you don't have an electric mixer, I say, invest in one. Liberally grease your foil-lined pan, however you decide to let it set, by spoonfuls or in a square. It makes release much, much easier. And finally, those two egg yolks you end up with afterwards? Freeze them in an ice cube tray, and save them for a curd later. This also goes for egg whites in other situations.

This is a dessert that most people find is perfect for a single bite. It's also great for those who want fudge, but can't have chocolate. I recommend trying it at least once, but make it for a party, because you won't want to eat the whole thing yourself.