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I (think) I get it. It seems pretty strait forward, but it takes a bit to get my head around.
Thanks for the speedy response, but more importantly, that for the lengthy and informative response.
My proof was really, really, flawed, does someone have one that works?
landof+ can you post your answer? JaineFairfax, I'd like to see your proof too.
It might help if you posted your work to date (even if it's wrong) then we can say, "there, that's where the mistake was made!"
Also, are you absolutely sure the answer is wrong? If you got the answer from the back of the book, it might be wrong, some books have an absurdly high error rate.
That is far better an answer than I would have expected, Ricky, thanks.
However, if you re-run that same problem, wouldn't you get the same "random" numbers? If not, then how? You said it's how my OS chooses to switch, won't it choose to switch the same way each time? Won't the cache gets hit (or not) the same each time?
My computer knowledge is pathetic at best, so please bare with me if some of my questions don't make sense.
These are fun, it takes a certain breed of humor to appreciate them, and I do.
Thus far the tvSize < desiredSize is the best.
You might want to double check your math there, bossk.
I do this all the time, I get it conceptually, I get all exited and ahead of my self, drop a few key points, and then make myself look like an idiot. Thanks for pointing it out before too many people see it, it's fixed now.
landof+ is correct of course, does any one want to show that those are the only values for a, b, and c?
bossk, you've never seen the proof that 1 + 2 + ... + n = n(n+1)/2? thats a piece of cake!
You're right, that's really straight forward.
I've read a few books where they tell a story that goes something like this:
When Guass (the famous mathematician) was just a kid at only eight years of age, the school teacher gave the kids the assignment of summing all the numbers from 1 to 100. The idea was to keep the students busy while the teacher did something else. Guass wrote down his answer within a few minutes of the teacher's assignment, where as all the other students were still summing at the end of the class, and Guass was the only one to get it right. What Guass had noticed (as an eight-year-old!) was that if he took all the natural numbers form 1 to 100 and added them to themselves [img]backwards[/img] you'll get a sum of twice what your looking for much easier to do:
1 + 2 + 3 + 4 + ... + 98 + 99 + 100
100 + 99 + 98 + 97 + ... + 3 + 2 + 1
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101 + 101 + 101 + 101 + ... + 101 + 101 + 101
Then dividing that sum by two, (10100/2 = 5050) Guass got the desired result. Using that story, most of the books launch into a lesson about how easy it is to see that's true for all natural numbers.
I like the proof more now, it's a real great example of how great induction is. Has anyone ever heard it called the ladder of thought before, or is that something exclusive to my calc teacher (he was a bit nutty)?
Also, as you put, the proof of (n(n+1)/2) = 1+2+3+...+n is "a piece of cake" if your dad is brushed up on his high school Algebra, he should have no trouble with it. And recommend the book Coincidences Chaos, and All That Math Jazz by Edward B Burger & Michael Starbird to your dad. Seasoned mathematicians might find it a bit stale, but it had some a lot of neat introductions for people who don't have much experience under their belt (and good sized section on the Golden Ration).
But a computer *could* have a true random number generator implemented in hardware, for truly "organic/biological" programs.
It could? That kind of brings me back to my original question of how...
Actually, I'm thinking of three numbers:
a,b and c are three consecutive numbers. a is prime, b is a perfect cube, c is a perfect square. What is a?
The answer would be good, props to proving that there's only one answer though.
Use Hide tags.
EDIT: I made a huge mistake when I posted this. It's fixed now. SORRY.
This has always bothered me:
How do random number generators work? I can't see how anything in computers can be random.
My two guesses are:
1. Take an irrational number (let's say pi=3.14159...) and when you use a random number function, it calls 3, then 1, then 4, then 1 and so on... giving the appearance of randomness.
2. Using really really small time intervals (beyond our perception) and designating them as values 0.001s = 1, 0.002s = 2, 0.003s = 3 etc. So when the random number function is called, at a certain time, a number is spat out based on the time it is called. This idea seems more flawed to me, but easier do.
So how is it really done? Can some one give me a good idea, or better yet, write something up in C++? Please keep it as simple as possible, I'm still pretty new at programming (relatively).
My Calc teacher always called induction the "Latter of Thought" The way he said was that if you can prove the first rung of the latter exists, and can assume that an arbitrary rung exists, then by proving that the rung above the arbitrary rung is there, you've proved that the entire latter exists.
It's not really saying more than what already been said in this thread, but I always thought that it gave a really good visualization.
As for the proof that 1 + 2 + ... + n = n(n+1)/2, I'd really like to see that. I've never actually seen a formal proof, instead that's always been presented to me in an intuitive way, starting with a story of Guass's childhood.
Also the second post down here by Dross is a really great FALSE proof by induction.
yo quiero hablar espanol, pero no hablo espanol. Soy muy, muy malo.
Quotient Rule (u/v)' = (vu'+uv')/v²
How does one do subscript without LaTeX?
it's suppose to llook like this:
Yes, I realize that, and I'm pretty sure that
If a line is perpendicular to another, it means their slopes are opposite reciprocals. That means that if one line has a slope of m and another is perpendicular to it, then the second line has a slope of -1/m
I imagine every text book has their own version of this equation, but I learned it as:
So we have
Therefore
Hey, Patrick Shambayati, I'm pretty sure we have the same sig.
What if she wants a double decker sandwich with 3 slices?
You could do 9 + 9/2 + 15/2 + 15, with the half slices in the middle.
Or, I could go out and buy a loaf of 6 grain bread (if it exists), and she could have two slices of 15 with one slice of 6:
6 + 15 + 15
EDIT: But that leaves the issue of using up the 15 grain at twice the rate of the 6. On second thought, your way is superior.
Not really a joke I guess because it really happened...
My mom sent me to the grocery store with a list today. One of the things she wanted me to get was 12 grain bread.
They were all out of 12 grain bread so I bought 9 grain and 15 grain and told her that when she makes a sandwich just to use a slice from each loaf.
She wasn't too impressed, but I thought it was kind of funny.
bossk171 wrote:The range is the lowest number and the highest number, 15,60
The range is the difference between the highest and lowest numbers, so its 45 in this case.
Thanks for correcting that, I guess I don't remember my mean median and mode stuff so well.
sin²x + cos²x = 1
Divide through by cos²x
tan²x + 1 = sec²x
Subtract 1 from both sides.
tan²x = sec²x - 1
5² = 5*5 = 25
The little 2 (that's call ed the exponent) tells you how many times to multiply the big 5 (the base). so 2³ = 2*2*2 = 8
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Sarada, first put your numbers in order:
15,17,25,32,45,46,60
The median is the middle number, 32
The mode is the number that appears most, because they all appear once, there is no mode.
The range is the lowest number and the highest number, 15,60
That's what I tried doing, but it got so messy, I gave up.
I guess I should have just committed.