We have a big game on Thursday (1/9/25). What are you doing to prepare?
- Thread starter BobPSU92
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I could talk about nipples in the context of algebraic topology, would that work for you?
Ring. You have both multiplication and addition. When you have just addition or just multiplication, it’s called a group. When you have a mental circle jerk, it’s a PSU BOT meeting.
x^2=x
x^2 - x = 0
x(x-1) =0
x=0 or x=1
If one of my students gave me that supposed proof, I give them a ZERO>
I'll also be logging out to watch the game. The inevitable avalanche of negativity that will accompany any play that does not go perfectly would only piss me off. The game will be four quarters, and the final score is all that matters.
This is true for the real numbers. The real numbers are a field (you can cancel) so anytime you multiply two numbers to get zero, one of them has to be zero. This isn’t true in general rings. As a simple example of this, suppose that you’re working in ZxZ, which is a ring consisting of all ordered pairs (x,y) where x and y are integers. Simple idea, you have elements like (3,2) and (-4,7) and you multiply and add component wise so that (5,7)+(4,2)=(9,9) and (2,3)(5,4)=(10,12). So you have (0,5)(2,0)=(0,0), the zero element in ZxZ, you have two non-zero elements multiplying to the zero element. Same thing with, say, Z_6. When you divide a number by 6, you get a reminder, right, and this reminder will be 0,1,2,3,4,5, right? So you just focus on the remainders and do the math from there. So you get 2+3=5 and 5+2=1 because 5+2=7 and when you divide 7 by 6 your remainder is 1. In the same way you get 2x5=4 (because the remainder you get when you divide 10 by 6 is 4) and 3x5=3 (because the remainder you get when you divide 15 by 6 is 3). In particular you have 3=3x5=3x1, and you cannot cancel the 3. Same way, you get 3x4=0 (because 3x4=12 and 12 is evenly divided by 6, the remainder is 0). You have two non-zero elements multiplying to zero. What you wrote is true in a field. The ring of real numbers is a field. Boolean rings are, in general, not fields.
Field (mathematics) - Wikipedia
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If you’re working in ZxZxZxZ, thenThis is true only for the real numbers. The real numbers are a field (you can cancel) so anytime you multiply two numbers to get zero, one of them has to be zero. This isn’t true in general rings. As a simple example of this, suppose that you’re working in ZxZ, which is a ring consisting of all ordered pairs (x,y) where x and y are integers. Simple idea, you have elements like (3,2) and (-4,7) and you multiply and add component wise so that (5,7)+(4,2)=(9,9) and (2,3)(5,4)=(10,12). So you have (0,5)(2,0)=(0,0), the zero element in ZxZ, you have two non-zero elements multiplying to the zero element. Same thing with, say, Z_6. When you divide a number by 6, you get a reminder, right, and this reminder will be 0,1,2,3,4,5, right? So you just focus on the remainders and do the math from there. So you get 2+3=5 and 5+2=1 because 5+2=7 and when you divide 7 by 6 your remainder is 1. In the same way you get 2x5=4 (because the remainder you get when you divide 10 by 6 is 4) and 3x5=3 (because the remainder you get when you divide 15 by 6 is 3). In particular you have 3=3x5=3x1, and you cannot cancel the 3. Same way, you get 3x4=0 (because 3x4=12 and 12 is evenly divided by 6, the remainder is 0). You have two non-zero elements multiplying to zero. What you wrote is true in a field. The ring of real numbers is a field. Boolean rings are, in general, not fields.
Field (mathematics) - Wikipedia
en.m.wikipedia.org
(1,1,0,1), (0,1,1,0) (1,1,1,1), and (0,0,0,0) are each solutions to x^2=x. In this case you would have precisely sixteen different solutions to x^2=x. In Boolean rings you can refine it even more so that every x is a solution to x^2=x. I would say that this is second year graduate level algebra.
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The bottom line, that everyone needs to understand, is this. We win one more game and we're in the National Championship game. We win two games and we're National Champions.
That's it.
Win Two Games
You've only seen one Superbowl run so I understand it's still new to you.
hehe
Fitting that melon into a football helmet had to be work yo .
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Last game I had to get up at 5am the next day. It was tough. This one - free and clear. The Yueng drafts will flow. Cold down here. Thinking about a mini beef-wellington. Going to Doris' market tomorrow. We'll see what I come back with.
If you have an hour to kill in the next two days, this week's episode is definitely worth a listen. Tengwall should have a bright future in sports media. As I mentioned elsewhere, I was dying at Tengwall's Cam Rising story. And thinking about Mike the Mailman drinking at G-Man with a 22 year old Al Golden also cracks me up.
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Your guarantee is the "kiss of death."
In fairness, Rick predicted way early that we’d be playing in the semifinals.
Additional things to do:
1) work out twice to relieve anxiety
2) watch copious amounts of film - mostly Woody Allen or Coppola
3) have a scone
4) apply face paint today as like a run thru - that will go over well with spouse I'm sure
I'll think of more later.
1) work out twice to relieve anxiety
2) watch copious amounts of film - mostly Woody Allen or Coppola
3) have a scone
4) apply face paint today as like a run thru - that will go over well with spouse I'm sure
I'll think of more later.
I don’t think I’ve ever seen the word wizz actually in writing. Fascinating
I have spent my time this week personally evaluating this Notre Dame team despite not knowing a single thing about Xs and Os. The conclusion I have come to is that Notre Dame is horrible and Penn State will crush them.
It's bad luck to have sex with me too. Just ask my wife.
Not available for in-person attendance myself so am sending friends, and I’ve encouraged them to announce themselves.