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Restless with a Random Question

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  • "Explain+how+to+prove+that+there+is+an+infinite+number+of+primes."

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    07-12-2012, 08:15 AM
  #1
Showing
Restless with a Random Question

Have you just not felt like sleeping in your bed before?

I have this weird inclination to pass out in this Laz-E boy chair all reclined and stuff with a blanket. I just feel I'm not going to be happy in my bed since lately I've been getting little to no sleep and it's frightfully cold...

Apologies if I sound crazy and you lot are stuck with me as my course is on hold due to the teachers being out of the office (seriously..) and I've downed more coffee and sugar today than I ever have in my entire lifetime so I think I'm going to be up a while..

And yes I have been creeping about on the forum lately... Wallaby knows why. The "math" they have assigned me has knocked a few screws loose. I feel crazier and crazier trying to interpret what on earth THIS means:

Quote:
If n itself is prime then there is a prime greater than p.
Suppose n is not prime, then there is a number m such that m > 1, m < n and m divides n exactly. Let q be the smallest such number.
Suppose q is not prime, then there would be a divisor r > 1 of q such that r < n and r divides n exactly, so q would not be the smallest such number. Thus q is prime.
Suppose q <= p, then q is one of the primes in the definition of n above, so n/q would equal an integer plus 1/q, which is impossible, since q divides n exactly. Thus if n is not prime then there is a prime greater than p.
Thus whether or not n is prime there is a prime greater than p.
Thus for any prime number there is a larger prime number, so there are infinitely many prime numbers.

There is a simpler proof, given in 1878 by the eminent mathematician Kummer:
Suppose the number of primes is finite: p1, p2, ..., pk, and let n be the product of all these primes. n - 1 > pk so is not prime, so there is some i such that pi divides n - 1. Since pi also divides n, pi divides n - (n - 1) = 1, which is absurd. Thus the number of primes is infinite.
All I need to answer is "Explain how to prove that there is an infinite number of primes" which I know how to but that piece of 'logic' from my course book is.......... conflicting.



Oh and I ate steak and cheese pie for dinner. That was lovely..
     
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    07-12-2012, 08:46 AM
  #2
Green Broke
My husband sometimes has issues sleeping in one spot and occasionally leaves the bed to go to the recliner or sofa (the sofa is cushy and reclines). For him it tends to be able the temperature of the room, which due to the way the house was built sometimes stays warmer than he'd like.

I, however, can fall asleep anytime, anywhere, regardless of I'm tired or not.
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    07-12-2012, 09:08 AM
  #3
Showing
Yeah that would make sense.. for me (this may sound odd) but it's just the bed itself plus the awful textured sheets. I used to have memory foam bed (so spoiled!) and now it's spring mattress with scratchy walmart sheets. Just not comfortable at all.

Thanks for your response :)
     
    07-12-2012, 09:17 AM
  #4
Showing
I often sleep on the couch instead of in my bed. Just depends on how I feel at the time.
     
    07-12-2012, 09:19 AM
  #5
Green Broke
If you're going to be there a while send someone to buy you a memory foam topper and some new sheets! This is a quality of life issue and those to me get ranked up high.
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    07-12-2012, 09:27 AM
  #6
Showing
Very true Dancing, did not consider that! I had to throw out my memory foam since coming here they didn't accept the fibers or something (they're very strict) so we'll see if I can get a nicer bed *topper temporarily..

Thanks SpeedRacer for contributing :) Once I slept on the bathroom floor because it was more fitting than my bed (hot hot night + cold tile floor = happy!)
     
    07-12-2012, 09:29 AM
  #7
Showing
I don't think I've slept on the bathroom floor since my 20s, during my debauched years of boozing and various other unsavory habits.
     
    07-12-2012, 09:38 AM
  #8
Showing
I always have intentions of sleeping in my bed but I do pass out on the couch occasionally. It's generally on nights I'm in the barn riding late, come in and shower, sit down and attempt to watch a show I've dvr'd and well, it just never works out...

LOL @ SR & the bathroom floor, had a few of those nights in my 20s too. I did lay down on my kitchen tile when I came inside last week during the 100+ hellish heat wave we had. My daughter thought I'd lost my marbles.
     
    07-12-2012, 09:40 AM
  #9
Trained
Worrying about prime numbers will keep you awake. In fact, it might make you break out in hives. I would not think about that stuff late at night. Read a lite novel before bedtime. Then just lay there and try to think about drifting clouds.............
     
    07-12-2012, 09:45 AM
  #10
Showing
Celeste you're very right..... I will stop trying to figure it out!!

Oh SR you are hilarious

You were smart, MH! I sometimes have to stick my face in the freezer to cool off in Spain due to the heat. Gotta do what you gotta do!
     

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