Rice used to have a cheer at football games (back in its days of even greater geekdom) that went like this: "Cosine Secant Tangent Sine 3.14159 Cube Root, Square Root, BTU Compass, Slide Rule, Go Rice U!" Just thought I'd share that little nugget.
Thats like the riddle with two schools with an infinite student body population trying to get rooms at a hotel with an infinite number of rooms. How do you fit all the students from both schools into the hotel? . . . . put all students from school 'A' in even numbered rooms and all students from school 'B' in odd numbered rooms. thats how you fit 2*infinity (in essence, also infinity... just reached at a faster rate) into infinity.
A more accurate representation of the theory is to use fractions. For example you could use 4/3 (1.3333333333333333333.....) and 7/3 (2.3333333333333333333......) Both numbers are infinite, yet you know the second number has a larger magnitude. I believe Descrates called them aleph 1 and aleph 2 You could do the same thing with negative numbers. Your discussion of negative numbers and positive numbers may be correct. But it's easier to explain using the fractions ( I think).
I think PSJ meant that, like Pi, it has an infinite number of decimal places. Anyhow, Descartes Geometry (which led to the Cartesian Coordinate System, right?) is being expressed wrong here, imo. By "Magnitude," he meant that a line of any magnitude has an infinite amount of Cartesian points. am I missing something here regarding the context of the word "magnitude" as used by Descartes? Thus you can have "different magnituds" of lines that each represent an infinite number of points.
I think heypartner is right. I recall the word catersian. I also recollect words like "continuity" and "set thoery" being used. But all of that is beyond me. I believe Cantor went insane trying to develop these theories This was 7th grade for me. Almost twenty years ago. So I can't take this any further
I got the point about the infinite number of digits, but not about the magnitude. If they both have an infinite number of digits, how does the fact that one starts with a 3, and one with a 4 make any difference? I must confess to being somewhat ignorant here though. I wasn't aware of a direct link between Cartesian geometry and varying magnitudes of infinity.
This is actually getting more interesting. I'm learning little by little. Although I'm going to screw this up, this is what I think I learned on the internet. The Hotel problem and the number line (1 to whatever) are exploring transfinite numbers and some thoery called the continuum. Infinity +1 = Infinity. Infinity x Infinity = Infinity. Crap like that. All of it related to different levels of Infinity of course. What I am discussing is related to linear infinity and cartesian coordinates. All of it related to some "smaller" infinity than the continuum represents. Such as an infinite amount of numbers between 1 and 2 versus the infinite amount of numbers between 2 and 3. Apparently, one of the great goals of mathematics is to discover what types of infinity lay between the Contiuum stuff and the linear stuff. Some believe that if you discover it you have discovered the nature of things. Whatever the hell that means.
It was described wrong. Descartes never said that there are varying magnitudes of infinity. He said that there are varying magnitudes of lines that have infinite points. nothing was described correctly regarding Descartes in this thread. He never said what was described.
"My man heypee has the part of my back not protected by my long early-modern mullet!" Descartes is actually the owner of a hilarious history. He loved to sleep late, but he got a job in Sweden as the royal mathematician, and Queen (Freak) Kristina loved to get him up at 5 a.m. to help her play geometry games. He was dead within one year of taking that job.
yeah we had that banner with pi on it in 5th grade. i recited it for some teachers one day. then during my senior year, we had pi day (march 14th) in our stats class and had a competition to memorize the most digits. i won with 271 and got 20 extra points on a test (of course it was senior year and grades didn't count anymore so i didn't care about that). i got it up to 370 in the car on a long trip once but then i just quit cuz it got boring. and 1.24 trillion, that's insane. i didn't even know they had passed 100 billion.
If this thread gets any nerdier, you all will start having a scientific discussion of Star Trek. "No...I'm telling you that the problem with the transporter was that the capacitor wasn't creating the proper beam array out of optic shaft 3." What? You have to be a REAL dork to "study" the "inner workings" of a fictional device. Ramble on fellas.
I remember being intrigued by Pi as a kid... wait... no... I didn't just say that. What I meant was that I remember reading about this beauty that loved Pi... no joke. Something about a beautiful woman with a beautiful mind : Eve Anderssen (the girl that loved Pi) http://www.ugcs.caltech.edu/~eveander/ http://www.ugcs.caltech.edu/~eveander/aboutme.html http://eveander.com/pics/ I emailed her once to correct something on her website... she corrected it, thanked me, and moved on to start a $25 million/year company. Not that my correction had anything to do with it, but hey...
