2 + 2 = 5

[Brad Barker]

I cannot put into words how completely useless div, curl and grad seemed in calc 3, and how incredibly necessary I know they are now that I've had my class that applies them. It's my Calc 3 prof's fault for not covering enough physical applications!!

I was thinking the same thing. Thank goodness Brad finally put an end to the madness

well, if my friend gets his way, in the future, all EM will be taught using differential forms, so we don't have to worry about this grad (1-form), curl (2-form), and div (3-form) nonsense.

actually, in my calc 3 class, we didn't make it to grad, curl, and div! we *just* got to line integrals. :scowl: (good thing i learned all of that stuff on my own before coming into college. )

in physics, any line or surface integral you do is set up so that you don't have to actually do an integral, so it all works out in the end.

 

[kydnav]

I'm a simple girl..
If you take a cake, slice it in three.
3 times 1/3 of a cake.
the 0,0(infinitely)1 are the crumbs you lose when slicing it

 

[ThatGermanDude]

I'm a simple girl..
If you take a cake, slice it in three.
3 times 1/3 of a cake.
the 0,0(infinitely)1 are the crumbs you lose when slicing it

i like the way you think

 

[Cerb]

Poor Winston learned this the hard way....(1984 reference)

But, at least he loved Big Brother.

 

[DayoftheGreek]

You guys are awful. Seriously.

A funny math essay thread turned into an argument over something like this? You should be ashamed.




However, that essay was pretty funny, I didn't expect it to be so long, but they had plenty of goofy example and hidden references.

 

[kydnav]

i like the way you think

I wish my math teacher liked it...

 

[Jeff Moote]

well, if my friend gets his way, in the future, all EM will be taught using differential forms, so we don't have to worry about this grad (1-form), curl (2-form), and div (3-form) nonsense.

That looks really cool, but I'm not entirely sure it's easier than the grad, div and curl operations. After all, with some knowledge of algebra and vector calculus, those operations are actually easy to work with.

actually, in my calc 3 class, we didn't make it to grad, curl, and div! we *just* got to line integrals. :scowl: (good thing i learned all of that stuff on my own before coming into college. )

Wow - where did calc 2 leave off that it took so long to get that far??

in physics, any line or surface integral you do is set up so that you don't have to actually do an integral, so it all works out in the end.

Yup, it's the same for us with engineering calculations (since it's all just applied physics stuff anyway). It's more solving of ODEs and PDEs than anything.

 

[Brad Barker]

That looks really cool, but I'm not entirely sure it's easier than the grad, div and curl operations. After all, with some knowledge of algebra and vector calculus, those operations are actually easy to work with.

yeah, that's what i think, too. if i were taking analysis II (graduate) and special topics in relativity like my friend was, maybe i'd be singing a different tune. he SWEARS it's easier, though!

brigham young university has some electrical engineering profs that have a hefty pdf trying to teach EM with differential forms, beginning with a basic introduction and stuff. i couldn't really get into it, myself.

Wow - where did calc 2 leave off that it took so long to get that far??

it was a normal calc 2 class. we covered how to do all sorts of nasty integrals, surface areas, sequences, series, convergence theorems, and all that. it was the calc 3 prof's fault that we didn't get to the fun stuff--other profs got through all the necessary material. it was his second semester teaching; he often gave homework assignments that were "do as many problems as you need to" because he couldn't decide on which problems to skip or not. (wasn't a problem for me since i have a decent idea of when i know something or not, but it tripped up a lot of classmates!)

Yup, it's the same for us with engineering calculations (since it's all just applied physics stuff anyway). It's more solving of ODEs and PDEs than anything.

i think the funniest thing about physics is that we don't even really seem to solve ODEs or PDEs. we just get to an equation, then whaddayaknow, bessel or airy or whoever has solved it two centuries ago, so let's just reuse his answers and not solve it ourselves!

my quantum professor said something like, "if we get a mess, then we just call the mess our answer!"

 

[Jeff Moote]

i think the funniest thing about physics is that we don't even really seem to solve ODEs or PDEs. we just get to an equation, then whaddayaknow, bessel or airy or whoever has solved it two centuries ago, so let's just reuse his answers and not solve it ourselves!

my quantum professor said something like, "if we get a mess, then we just call the mess our answer!"

Right, well that's my idea of solving equations - having a table of solutions for various forms. I guess I'm still at the point where they want us to demonstrate other methods too, but it's never too hard (hurrah for Laplace transforms )

 

[jenderfazz]

If we assume that 0.33333... = exactly 1/3, then we must assume that 3 x 0.33333.... = 3 x 1/3, which is equal to exactly 3. Thus, 3 x 0.333333.... = 0.99999.... = 1.

If we can't accept that, then we can't accept that 0.333.... is exactly 1/3. Thus, it's just a rounded number, and you aren't getting at the true value of 1/3.

But the proof posted beforehand is even better.

I love these debates, even though I can't often contribute much.

 

[soulgeezer]

I may be way off on this (I truly suck at math, but I have a pretty good notion of how to apply it to real life), but fractions are not decimals and cannot be precisely expressed as decimals in many cases.

Look at it this way: Take a piece of paper and cut it in thirds. Now, measure the thirds. I'll bet those thirds are not 0.3 of the original size of the paper. In fact, I'll bet those thirds are more like 0.3 + (1/3 x 0.3) of the original size!

This is why I hate math. This, and algebra. What does X equal? Nothing! It's just some kind of sleight of hand performed by a mathematician.

Want proof? Think about multiplying fractions. First, Junior, invert the second fraction...

WHAT!?! But, then it's not the same number!

Oh, it doesn't matter; this is how math works!

 

[Jeff Moote]

I may be way off on this (I truly suck at math, but I have a pretty good notion of how to apply it to real life), but fractions are not decimals and cannot be precisely expressed as decimals in many cases.

Look at it this way: Take a piece of paper and cut it in thirds. Now, measure the thirds. I'll bet those thirds are not 0.3 of the original size of the paper. In fact, I'll bet those thirds are more like 0.3 + (1/3 x 0.3) of the original size!

This is why I hate math. This, and algebra. What does X equal? Nothing! It's just some kind of sleight of hand performed by a mathematician.

Want proof? Think about multiplying fractions. First, Junior, invert the second fraction...

WHAT!?! But, then it's not the same number!

Oh, it doesn't matter; this is how math works!

It sounds to me like you just have no idea what is going on with math

 

[Tom Crofts]

Got to admit, when I saw the heading of this thread, I was afraid someone one beat me to it, but so far you guys are arguing mathematics. Big relief!!

2+2=5 is my contribution to society, you see. At least I hope it to be. And all of you, the most exalted members of TalkBass, may join me in my crusade to establish this phrase into common everyday usage. All you must do, is next time you speak of someone who came to the wrong conclusion,or imagined there to be more to a situation than the facts supported, simply say, " He/She put two and two together and came up with five!"

I believe we can change the world if we keep at it, and eventually everyone will start to use this phrase. When that day comes, we will remember where it all began, right here in the hallowed halls if TalkBass. Thank you. Go forth and multiply.

People have been saying that for some time... It's a pretty standard expression, sorry to disappoint you.

 

[Vandelay]

First shalt thou take out the Holy Pin. Then shalt thou count to three, no more, no less. Three shall be the number thou shalt count, and the number of the counting shall be three. Four shalt thou not count, neither count thou two, excepting that thou then proceed to three. Five is right out. Once the number three, being the third number, be reached, then lobbest thou thy Holy Hand Grenade of Antioch towards thy foe, who, being naughty in my sight, shall snuff it.

 

[SOA_bassist]

I always thought that the 0.3333 ( 3 for infinity ) was only written as that because there is no way to write 1/3 as a decimal, and that if there was a proper way to write it as a decimal then it would have an end.

basically ( with how I am thinking of this ) the only true way to write 1/3 as a decimal would be to find a way to write things in much smaller terms, and get back what you lost through the conversion.

for example, it shouldn't be written 0.333 +0.333+0.333 but 0.3 + 0.3 + 0.3 + 1/3 of 0.3 which got lost through the conversion.

Its not 0.9999 = 1 but 0.9 + the 0.1 that was taken away through conversion = 1.

And you can also think of it as cutting a rope. You take a rope that is 100 cm long and you want to cut it into three equal pieces, which are all 1/3. Do you cut them down to 33 centimeters each or 33 cm and 1/3 of a cm each? If this one just isn't complete correct or doesn't get my point across read my next example.

You have 100 square pieces of paper, measuring 3 inches by 3 inches. You want to divide it into 3 equal piles. Do you just make 3 piles of 33 pieces of paper? no. you make 3 piles of 33 pieces of paper, cut 1 piece into 9 pieces that are of equal size, and put three pieces of it in each pile.


And yes, it is 6:23 AM as I am typing this and I haven't slept all day, so if I made a major mistake, I am sorry. Point out all of my fallacies. I know that this is somewhat of a paradox, and I am probably very confused about all of this.

 

[Loose Cannon]

People have been saying that for some time... It's a pretty standard expression, sorry to disappoint you.

That means it has caught on! I started this 20 YEARS ago or more, seriously!
But...no-one around here uses it....guess they are still ignoring me...

 

[bigfatbass]

Um, there is no big question here.

Decimal representations of fractions of a whole are occasionally imperfect (0.6666666, 0.3333333 whatever).



This is not a great mathematical debate, it is just an inherent flaw in the decimal system. It doesn't require calculus or three pages of babble to see that.

 

[Jeff Moote]

Um, there is no big question here.

Decimal representations of fractions of a whole are occasionally imperfect (0.6666666, 0.3333333 whatever).



This is not a great mathematical debate, it is just an inherent flaw in the decimal system. It doesn't require calculus or three pages of babble to see that.

Exactly. Plus, if you do notate repeating decimals, 0.333 repeating is exactly equal to 1/3, and 0.999 repeating is exactly equal to 1.

I think that's where the argument started, but nobody saying otherwise is going to win.

 

[Obese Chess]

interesting side note: one of my friends used perfectly logical mathematical stuff to 'prove' that 1=2. A calculus professor couldn't find anything wrong with his math.

 

[CrazyArcher]

Hmm, one can build a function (N->R), that returns for each x 0.3333..., with number of 3's after the decimal point equal to x. So, well, the function won't return 1/3 for any x in the domain, but its limit in the infinity will be 1/3... Well, I like functions

Another point of view is one of an engineer: 0.999999... is pretty close to 1, so no one will ever notice, meaning that the approximation is good enough