I would like to prove [0,1], as a subset of R with the standard Euclidean topology, is compact. I do not want to use Heine Borel. I was wondering if someone could check what I've done so far. I'm having trouble wording the last part of the proof.
Claim: Let \mathbb{R} have the usual...
The reason I have that in quotes is because by definition, elements in a set must be unique, and there is no concept of repeated elements. I was just wondering if there is a word to describe such an object - namely, a collection of "items" (or whatever you'd like to call them), where you might...
Thanks PeroK, as long as I know the problem statement is a little ambiguous, I feel better. As for (2), I'll play around with it, I just wasn't sure if there was just a super common formula that I just didn't know which is why I had asked.
Thanks for all the help, especially since it took me...
ok, this does make sense when you put it this way! Thank you very much :)Two follow up questions -
(1) If you were to see the original problem statement (how many ways to write 4 as the sum of 5 non-negative integers?), which version would you jump to, the one where order matters (where you...
I have to be honest, I feel like a bit of a dunce here because I don't seem to understand what the problem is even asking :( I'm sorry to be beating a dead horse.If this is what it is asking ("how many solutions are there to the problem x_1 + x_2 + x_3 + x_4 + x_5 = 4, where x_1, x_2, x_3, x_4...
So you're saying the problem is, assume x_1, x_2, x_3, x_4, and x_5 are 5 numbers such that when you add them together, they equal 4, and the problem in the book is asking: how many different ways can we select sets of 4 of these variables, where repeats are allowed? (so in their analogy, each...
This is where I'm struggling. Based on my understanding, 0-2-1-1-0 is equivalent to the "answer" 2 + 1 + 1. But how would the answers 0-2-1-1-0 and 2-1-0-1-0 be different from each other? This is where I'm failing to see the 1 - 1 correspondence, as both are valid combinations that would come...
Hi PeroK, perhaps you could elaborate a little bit, because this is where my disconnect is happening.
I understand that in a "combinations" problem (as opposed to a permutation problem), the order doesn't matter, and so repeats come out in the calculation. My confusion is seeing how their...
Oops, yes it seems in the examples I gave I was using 5 rather than 4. That was just a dumb mistake on my part. But if I redo the examples using 4 balls, I still have the same problem right?
(example - "box 1" 2 times, "box 2" 2 times and all the rest 0 equates to 2 + 2, "box 3" 2 times, "box...
the problem:
In how many ways can we write the number 4 as the sum of 5 non-negative integers?I realize this is a generalized combinations problem. I can plug it in using a formula, but I want to understand the logic behind why the generalizaed combination formula works. More specifically, my...
*combinatorics*, sorry for the typo in the title. The problem is as follows: In how many ways can we write the number 4 as the sum of 5 non-negative integers?
I have taken a screen cap of the solution that my book provides. Here it is
http://imgur.com/8BhxXPq
So I understand the concept of...
Sure. So if the task is to determine how many colored 5-ball subsets are possible using a tub of yellow, red, and blue colored balls, this would be (using the formula on this pdf http://www.csee.umbc.edu/~stephens/203/PDF/6-5.pdf):
C(5 + (3-1), 5) = C(7,5) = 7!/(5!(7-5)!) = 7!/(5!2!) =...
Note, this is not a homework problem, as I'm not even in college. I just had a quick question.
I know the formulas to do things such as "How many ways could you choose 5 balls from a tub of yellow, red, and blue colored balls?" (where you envision in this case, a tub where there's more than...