So does anyone want to fight over if a zero ring is a real ring or not
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07-22-2015, 10:53 PM #5491
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07-22-2015, 10:56 PM #5492
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07-22-2015, 10:56 PM #5493
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07-22-2015, 11:06 PM #5494
- Join Date: Mar 2008
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Agreed. As you know, ring theory is an equational theory so its axioms are negation-free and the consequences of negation-free statements are equivalent to negation-free statements. Equational theories can be interpreted in any category with finite products so that’s how, say, topological rings work - they are ring objects in top
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07-22-2015, 11:16 PM #5495
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07-22-2015, 11:29 PM #5496
So my muli-variable calc teacher briefly went into "differential forms"......sounds interesting but it's also confusing as hell. "Wedge Product" "0-form, 1-form, 2-form" ...........u wut m8? I looked at it some more on wikipedia and i saw some familiar words such as "pull-back" "push-forward" etc from reading the conversations between MiscMathematician and YokedBrah.............
dude I don't know how you go from doing multi-variable calc/diff eq/linear algebra and then jump straight to fukking differential geometry and topology. Chit is insane.**30 tabs open and can't tell which one the sound is coming from crew**
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07-22-2015, 11:31 PM #5497
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07-23-2015, 04:52 PM #5498
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07-23-2015, 05:57 PM #5499
ayyy! congrats man!
It's not too bad of a class, I have 100% between the first midterm and 5 homework assignments lolol.... I don't find it too interesting though. Analysis is a lot harder, and more interesting but honestly I never thought I'd say that I'd miss Group Theory. Group Theory/Ring Theory much more entertaining than Analysis/Number Theory imo.Trading/Investing Thread Crew
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07-23-2015, 06:48 PM #5500
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07-24-2015, 12:30 AM #5501
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07-24-2015, 01:03 AM #5502
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07-24-2015, 04:23 AM #5503
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07-24-2015, 05:43 AM #5504
That feel when you go on a hiking trip and the weather decides to be a bish...
We'll probably stay at the motel and get drunk today, fml.
Das it mane.
I've put off sending out resumes until October/November since I'm hoping to hear back about a few of my articles by then, but job-search time is looming for me too. Peppering angus.Ex-Ex-Fatass crew
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07-24-2015, 10:56 AM #5505
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07-24-2015, 11:02 AM #5506
Seems weird you'd lose points for that as you showed the calculus and the last step if just an algebraic simplification.
Just multiply them together. The RHS quantity cubed is equivalent to the cube of the numerator and the cube of the denominator.
So (24*(x-3)^3)/(x+3)^5Trading/Investing Thread Crew
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07-24-2015, 11:04 AM #5507
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07-24-2015, 01:47 PM #5508
So I'm looking at a solution to a problem and they knew that a^4=1 (mod4) and a^2=1 (mod2) and from knowing these two things they jumped from a^6=1 (mod8)
Anyone know what property they used here? I can't seem to figure out why this is legal.Trading/Investing Thread Crew
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07-24-2015, 03:27 PM #5509
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07-25-2015, 01:59 AM #5510
I think it would be difficult to use 'properties' (though am willing to stand corrected).
Note a^6 - 1 = (a^2)^3 - 1 = (a^2 -1)(a^4 + a^2 +1)
Similarly, a^6 - 1 = (a^3)^2 - 1 = (a^3 -1)(a^3 +1)
It's not clear to me how to show any of these factorisations is divisible by 8 without considering the parity of 'a'.Last edited by DesEsseintes; 07-25-2015 at 03:23 AM. Reason: too early in the morning here
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07-25-2015, 11:03 AM #5511
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07-25-2015, 12:04 PM #5512
Any advice for proving continuity in greater generality than individual points? I've been proving functions are continuous at specific points. Now on my homework I have two functions that are piecewise defined from R-->R and I'm asked to determine at which points the function is continuous and then prove it's continuous at these points and prove it's not continuous at all other points.
For example, one of the functions is x+1 for all x>=2 and 3-x^2 for all x<2. Intuitively I know this is certainly continuous everywhere but at x=2. So this means I need to prove it's continuous everywhere else which I'm not sure how to do since we've only been proving individual points and now I have an infinite number.
edit: I found a good article online that has better examples than my text so let me try a little longer. I think I can figure it out now.Trading/Investing Thread Crew
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07-25-2015, 01:00 PM #5513
Need some advice guys..........
There's one student that is really smart but really annoying; He interrupts teachers and sometimes argues with them. Even the most patient teachers groan when he begins to open his mouth. He once interrupted a student in the middle of her presentation (in a govt class) and this student told him to die. He still hasn't gotten the clue. I'm glad that he's so perceptive that he can instantly think outward about new material but when the class turns into an hour of his stream of consciousness.....it hinders my ability and everyone else's ability to learn anything. I've only had one class with him and I had to drop it. I'm gonna have 2 classes with him next semester and I'm already dreading it.
How should I deal with this? Who can I talk to? Should I talk to the professors in private and express my concerns about this student? The dean? etc...?
I feel like teachers should exercise their right to ask students to leave their classes. It's not nearly done enough.**30 tabs open and can't tell which one the sound is coming from crew**
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07-25-2015, 01:58 PM #5514
Okay I'm stuck and need to go eat something.. I think I have shown that f(x) is continuous on R\{2}. Now I just need to show that f(x) is discontinuous at x=2, however, for whatever reason I haven't been able to do this rigorously. I think I want to do some sort of contradiction based on the Sequential Characterization of Limits or the theorem that says the limit as x approaches a limit point equals L iff the limit as x approaches that limit point from the right and left equals L... However, I've failed miserably at actually producing a proof for this.
Is my proof for f(x) being continuous on R\{2} okay? How do I finish? I don't have an actual definition for discontinuity yet so I think I just need to use one of the two theorems above and do a contradiction but this hasn't worked for me :/
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07-25-2015, 04:04 PM #5515
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07-25-2015, 04:05 PM #5516
Thanks for the comments. You're absolutely right, that is a huge blunder on my part, the x>2 and x<2 should be x_0>2 and x_0<2.
My first step is always looking for an appropriate delta but I omitted that work for some reason. When I do a more formal write up for the hw I should probably leave it on there at the top to see where I'm pulling numbers from.
So I had two cases,
x_0>=2:
When I search for the delta 1 I get
|x+1-(x_0+1)|=|x-x_0|<epsilon
so choose delta=epsilon
x_0<2:
When I search for the delta 2 I get
|3-x^2-(3-x_0^2)|=|x+x_0|*|x-x_0|
If |x-x_0|<1, then |x+x_0|<1+2|x_0|
So, |x+x_0|*|x-x_0|<|x-x_0|*(1+2|x_0|)<epsilon if |x-x_0|<epsilon/(1+2|x_0|)
Then choose the actual delta to equal the min(delta1,delta2)=delta2
This is all the work I omitted. This should clarify all my "leaps" in the proof I uploaded.
EDIT:
I'm just going to write it up again how I would write it up for my Hw assignment. That way it'll be the best work I can do on my own, and then if somethings still off it won't be because I'm lazy, it'll be because I didn't understand it well enough.Last edited by ctownballer04; 07-25-2015 at 04:16 PM.
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07-25-2015, 04:33 PM #5517
However, I'm still very confused on the contradiction.
I see what you're saying about choosing epsilon less than the distance of the jump discontinuity, that makes sense from a geometric perspective. My confusion revolves around the structure I guess.
I just don't know what I'm even setting up I guess. Maybe through example I can explain my confusion better than in words.
So choose epsilon=1
|f(x)-L|<1
I don't know what I'm setting up since i have two portions of a piece wise function. So am I not guessing a limit? Am I keeping it arbitrary?
So something like:
|x+1-L|<1
and
|3-x^2-L|<1
and then try to show that there doesn't exist a delta where |x-2|<delta and this holds
I don't think this post makes any sense lol.
Last edited by ctownballer04; 07-25-2015 at 04:40 PM.
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07-25-2015, 04:52 PM #5518
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07-25-2015, 05:41 PM #5519
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07-25-2015, 06:39 PM #5520
ughh..
I've been reading this post for nearly an hour now and I'm still confused.
I have like three questions:
1) I don't really follow this let d=min(1,d) maneuver you did.
2) @Bold, what was the point of saying 3/4<1, I don't know where this one came from.
3) This is sort of in addition to question 1, but when you say d=min(1,d) and then use the assumption that d<1, isn't this fixing d, which would invalidate our proof since we need to show this can't work for any d?
I really appreciate the help man. I think I'm about to call it a night from math, maybe tomorrow will go better.. This class is so frustrating to me, I started doing math nearly 8 hours ago and I finished one problem on my homework set -_____-. I'm not cut out for this chit.Trading/Investing Thread Crew
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