Author Topic: The Math Lovers Club v. 3.1416  (Read 35455 times)

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Offline ich bin besser

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Re: The Math Lovers Club v. 3.1416
« Reply #140 on: November 20, 2011, 04:53:47 AM »
Maybe I should write it down without the coordinates stuff.

A = infinite

First: (((1000-(1/(A/200)))/3)*2,661)

Second: ((((1/A)^2)/4)+2)

1/infinite = 0, that's what the internet says. But infinite/200??
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Offline Jamesman42

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Re: The Math Lovers Club v. 3.1416
« Reply #141 on: November 20, 2011, 06:16:07 AM »
If A = infinity, then:

First: 887000

and

Second: 2


I did this by hand but since I have a lot to do, here is wolfram's interpretation:

First

Second

Offline Jamesman42

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Re: The Math Lovers Club v. 3.1416
« Reply #142 on: November 20, 2011, 06:21:25 AM »
Argue that ∃x∀yP (x, y) → ∀x∃yP (x, y) is not a tautology.

This is symbolic logic.

"If there exists an x for every y in P(x,y)[unsure what is meant by P(x,y) right now...elaborate?], then for every x there exists a y in P(x,y) [my guess as to how to say P(x,y)"

What method are you using on this? I dunno if I can help.

Someone is borrowing my logic textbook damn it. I've never actually taken a class on logic though I learned truth tables in one class...and I think this is one of those things just beyond what I know.

Offline kári

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Re: The Math Lovers Club v. 3.1416
« Reply #143 on: November 20, 2011, 06:38:36 AM »
No, it says "If there exists an X so that for every Y P(X,Y) is true then for every X there will exist an Y so that P(X,Y) is true". This is of course not always true, say P(X,Y) is "x^y = 0 with x any real number, and y any real number but not 0". Then the first half is true, there exists an x so that for every y: x^y = 0 (x=0). The second half is not true, if x = 1 for example then no y can make x^y = 0.

The condition that y =/= 0 is because 0^0 = 1 making the first part untrue.

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Offline Jamesman42

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Re: The Math Lovers Club v. 3.1416
« Reply #144 on: November 20, 2011, 06:46:04 AM »
What symbol talks about the truth of P(x,y)? Like I said, I've never taken a class on this, but I don't know where you would get that from.

Also, I think when he has to argue this,  he has to use some sort of actual method, not explaining with examples.

Offline ich bin besser

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Re: The Math Lovers Club v. 3.1416
« Reply #145 on: November 20, 2011, 06:53:11 AM »
If A = infinity, then:

First: 887000

and

Second: 2


I did this by hand but since I have a lot to do, here is wolfram's interpretation:

First

Second


Thank you - you were right!  :tup :tup

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Offline Jamesman42

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Re: The Math Lovers Club v. 3.1416
« Reply #146 on: November 20, 2011, 06:55:32 AM »
 :tup

Offline Jamesman42

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Re: The Math Lovers Club v. 3.1416
« Reply #147 on: November 20, 2011, 07:00:44 AM »
Oh, I think I see why...if-then statements already suppose that "If p is true, then q is true." I always just learned it as "If p, then q" and forgot about the truth values.

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Re: The Math Lovers Club v. 3.1416
« Reply #148 on: November 20, 2011, 07:08:40 AM »
Yeah, but normally it should be ∃x∀y: P(x, y) → ∀x∃y: P(x, y) to make it more clear. If you fill in P(x,y) you see why there should be nothing talking about the truth of it
∃x∀y: x^y=0 → ∀x∃y: x^y=0. The fact that the proposition is there makes it true. You know? :D

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Offline Jamesman42

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Re: The Math Lovers Club v. 3.1416
« Reply #149 on: November 20, 2011, 07:16:00 AM »
Haha yeah! It slipped my mind because I was just literally reading each symbol.

Logic is not my breakfast. I should go eat something. :lol

Offline Orbert

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Re: The Math Lovers Club v. 3.1416
« Reply #150 on: November 20, 2011, 07:28:56 AM »
Gah!  I hate those "Facebook Questions" with simple math problems that no one gets right.

40 + 40 x 0 + 1 = ?

Choices were 1, 41, and 81.

Left to right, ignoring order of operations gets you 1.  Most popular answer because no one remembers order of operations.
Correct answer obviously is 41.
Second most popular answer is 81?!  How in the fuck do you even get 81?!

I had people actually giving me shit for getting the right answer.  "I thought you were a math major".  Yeah fuck you, I was a math teacher for six years, which is why I know the right answer while you stuck your head up your ass somewhere in junior high and haven't pulled it out yet.

Then I explain order of operations (yeah yeah, the Internet, but Facebook is different because I actually know these people) and they're all "Wow, you're so smart" and I can't tell if half of them are being sarcastic or what.  Damn, I need smarter friends.

Offline Jamesman42

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Re: The Math Lovers Club v. 3.1416
« Reply #151 on: November 20, 2011, 07:33:44 AM »
Orbert, you should have seen the shit storm from that one ambiguous arithmetic problem we had a while back; I talked about it on facebook. I had people down my throat saying I was wrong for saying "you do multiplication and division left to right after parentheses and exponents." Except all my math buddies. They were on my side. :lol

Offline 73109

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Re: The Math Lovers Club v. 3.1416
« Reply #152 on: November 20, 2011, 10:13:50 AM »
Had a Calculus test on Friday. Pretty sure I killed it.

Offline kári

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Re: The Math Lovers Club v. 3.1416
« Reply #153 on: November 20, 2011, 10:34:36 AM »
Nice!

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Offline tjanuranus

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Re: The Math Lovers Club v. 3.1416
« Reply #154 on: November 20, 2011, 10:46:10 AM »
Oh, I think I see why...if-then statements already suppose that "If p is true, then q is true." I always just learned it as "If p, then q" and forgot about the truth values.

Math in the morning woooo

I just picked that off the net because I have to take that class in a couple semesters and it looks crazy to me! lol. Wanted to see the responses it got in here. It's for discrete math.

Offline Jamesman42

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Re: The Math Lovers Club v. 3.1416
« Reply #155 on: November 20, 2011, 10:47:42 AM »

Offline kári

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Re: The Math Lovers Club v. 3.1416
« Reply #156 on: November 20, 2011, 10:50:36 AM »
It's pretty easy if you have some mathematical insight. Near impossible if you don't.

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Offline tjanuranus

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Re: The Math Lovers Club v. 3.1416
« Reply #157 on: November 20, 2011, 10:52:11 AM »
Gah!  I hate those "Facebook Questions" with simple math problems that no one gets right.

40 + 40 x 0 + 1 = ?

Choices were 1, 41, and 81.

Left to right, ignoring order of operations gets you 1.  Most popular answer because no one remembers order of operations.
Correct answer obviously is 41.
Second most popular answer is 81?!  How in the fuck do you even get 81?!

I had people actually giving me shit for getting the right answer.  "I thought you were a math major".  Yeah fuck you, I was a math teacher for six years, which is why I know the right answer while you stuck your head up your ass somewhere in junior high and haven't pulled it out yet.

Then I explain order of operations (yeah yeah, the Internet, but Facebook is different because I actually know these people) and they're all "Wow, you're so smart" and I can't tell if half of them are being sarcastic or what.  Damn, I need smarter friends.

it's clearly 81. LAWL! People are crazy.

Offline Jamesman42

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Re: The Math Lovers Club v. 3.1416
« Reply #158 on: November 20, 2011, 10:55:33 AM »
I think people got 81 by adding 40, 40 and 1 and regarding 0 as adding nothing. That's my best guess

Offline ZBomber

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Re: The Math Lovers Club v. 3.1416
« Reply #159 on: November 20, 2011, 10:58:12 AM »
I hate those things. I suck at math and yet I know the answer is obviously 41.

They must not teach people the order of operations anymore.  :P

Offline tjanuranus

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Re: The Math Lovers Club v. 3.1416
« Reply #160 on: November 20, 2011, 10:59:43 AM »
I think people got 81 by adding 40, 40 and 1 and regarding 0 as adding nothing. That's my best guess

Probably. So you never had Discrete math?

Offline Jamesman42

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Re: The Math Lovers Club v. 3.1416
« Reply #161 on: November 20, 2011, 11:01:58 AM »
I've never taken it specifically, but I have learned many parts of it in other classes. Over the summer I worked at the college and they were offering it there and while I couldn't audit the class due to my other job, people from the class would come to me for help and most of it wasn't out of my reach.

I would still like to take the class, though, just to get better enriched in it. It's the one lower level math class I have not taken.

I could also stand to do well with a retake in Statistics. I am not good in that subject.

Offline kári

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Re: The Math Lovers Club v. 3.1416
« Reply #162 on: November 20, 2011, 11:07:39 AM »
I had this class last year called "Proving and Reasoning".

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Offline tjanuranus

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Re: The Math Lovers Club v. 3.1416
« Reply #163 on: November 20, 2011, 11:10:34 AM »
I will probably have to take Discrete math and Linear Algebra in the same semester... yay  :'(

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Re: The Math Lovers Club v. 3.1416
« Reply #164 on: November 20, 2011, 12:04:06 PM »
I hated Linear Algebra at first but I love it now. Let me know if you need any help. :)

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Offline Jamesman42

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Re: The Math Lovers Club v. 3.1416
« Reply #165 on: February 09, 2012, 08:38:04 PM »
Anyone good with some tough complex numbers involved with algebra stuff? I'll post the problem asap

Offline SystematicThought

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Re: The Math Lovers Club v. 3.1416
« Reply #166 on: February 09, 2012, 08:59:01 PM »
I told my Pre-Calc teacher why I suck at math and the bad experience I had and he seemed genuinely sad.

Basically in third grade when we first learned multiplication, I was asked 8x7. I had no idea and when I couldn't get the answer, the teacher backhanded me on the back of the head and kicked me out of class. That was fuckin rough. But that's Catholic school for you
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Offline Jamesman42

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Re: The Math Lovers Club v. 3.1416
« Reply #167 on: February 09, 2012, 09:26:36 PM »
So I just tutored a student in IB Math (hard stuff from what I hear) and he gave me a problem unlike anything I have seen involving complex numbers. I'm not pretending to be Mr. Math Genius here, but this is what I did. He showed me what was given and the first step of the proof. I think all the work is correct but the very last line doesn't make sense to me with |z| = 1 (I only know the very basics of complex numbers, or, maybe I don't if this is a basic). Here is everything you should need:




I figured that because of my final equation x^2 + y^2 = 1, the implication was that there was a circle of radius 1 correlated to the |z| = 1, but I do not know the connection. Any help would be awesome, would love to see how this ties together.

Also, I am unsure of why we need to use Im(w) = 0.

Offline theseoafs

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Re: The Math Lovers Club v. 3.1416
« Reply #168 on: February 09, 2012, 10:45:58 PM »
What exactly is it that you're confused about? The work looks good to me.

Offline Jamesman42

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Re: The Math Lovers Club v. 3.1416
« Reply #169 on: February 09, 2012, 10:47:43 PM »
Why do we go from knowing x^2 + y^2 = 1 to |z| = 1, and why do we need to use Im(w) = 0? These seem like concepts related directly to complex number properties and concepts, but I never learned.

Offline theseoafs

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Re: The Math Lovers Club v. 3.1416
« Reply #170 on: February 09, 2012, 10:54:36 PM »
The absolute value of a complex number x+yi is defined as sqrt(x^2+y^2), so if

x^2 + y^2 = 1
sqrt(x^2+y^2) = sqrt(1) = 1 = |z|

The absolute value of a complex number is fundamentally related to the Pythagorean theorem and linear distance; what you've found here is that the distance from the origin to that point on the complex plane is 1.

Im(w)=0 is essential so that we can set 2wxyi = yi, as you did. We can only make this relation, I think, because we're sure the two terms cancel.

If you never invoked Im(w)=0, how did you (correctly) know that 2wxyi = yi?

Offline Jamesman42

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Re: The Math Lovers Club v. 3.1416
« Reply #171 on: February 09, 2012, 11:01:51 PM »
Ohhh, ok, that makes sense, because absolute value tells us the distance from the origin to the complex number in the complex plane. Awesome.

And regarding the other point, I just figured that if you had real and imaginary parts on both sides, that they were respectively equivalent. It still doesn't make sense to me, though, about Im(w)=0 being involved. :lol If you can explain it further, that'd be awesome, if not I'll research it because this was fun to figure out.

Edit: I never actually learned what Im(w) = 0 meant though. It means the imaginary part of w, right? If so, yeah, totally lost on that point.

Offline theseoafs

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Re: The Math Lovers Club v. 3.1416
« Reply #172 on: February 09, 2012, 11:16:38 PM »
Im(w) = 0 means that the imaginary part of w is 0; in other words, that w is a real number, or that there are no terms in w with i.

So we have:

w(x^2+2xyi-y^2+1)=x+yi
wx^2+2wxyi-wy^2+w=x+yi

At this point, taking into account that Im(w) = 0, we know that once this has been simplified, the terms 2wxyi and yi will have canceled, since w cannot have any i's anywhere. And they will only cancel if they are equal, given that they're on opposite sides of the equation. So

2wxyi = yi
2wx = 1
w = 1/2x

Basically, you did exactly what you were supposed to do (you set these two terms equal to each other), but you can't just do that; essentially, you got lucky.  :lol

Does that make sense? Keep in mind that I'm still only in calculus, and I haven't had any in-depth study of complex numbers myself, so I could very well be wrong. (Hopefully, I'm not, but I embrace the possibility.)
« Last Edit: February 09, 2012, 11:24:10 PM by theseoafs »

Offline Jamesman42

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Re: The Math Lovers Club v. 3.1416
« Reply #173 on: February 09, 2012, 11:30:00 PM »
That makes a ton more sense, though it still needs to sink in for me to really get it (which is nothing on you, that's just me). Awesome explanation, I think it holds its weight.


This stuff wasn't covered in my precalc book, so yeah I had no idea. This is deeper than my studies and precalc book go. >:(

Offline theseoafs

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Re: The Math Lovers Club v. 3.1416
« Reply #174 on: February 09, 2012, 11:57:42 PM »
Anyway, I might as well formally introduce myself to the Club. I'm a first-year at the University of Chicago. I'm a computer science major, but I'm going to have to take plenty of math in the next few years. It's not my favorite thing, but I do like it and I have at least a little bit of a knack for it.