Unity+

I am assuming that this is a recursive function. a(1) would be a(n) a(3) would be a(n+1) Therefore, a(3) = (1+3)/2 = 2 If you notice, one of them is already a(2). a(1) = 1 a(2) = 3 a(3) = (1 + 3)/2 = 2 a(2) = 3 a(3) = (1+3)/2 = 2 a(2) = 3 a(3) = 2 etc. etc That is how I interpreted the problem.

Well, I live in Oregon. Therefore, if this happens suddenly... So Long, and thanks for all the fish.

You could make the joke that their union makes the golden ratio as it is a perfect match?

Forgiving such a high debt would lead to some economic issues, I would think. There would be major inflation in nations that lent the money, would it not?

So, I am beginning to apply for internships, and I was wondering what the difference between unpaid and paid internships in regards to environment and how effective they are on internships. Just give a general explanation, in those regards, of the differences between unpaid and paid internships.

From my understanding of vectors and matrices, here is the standard format when doing operations on vectors in matrix form. [math]\begin{bmatrix} A & B &C \\ x_{1} &x_{2} &x_{3} \\ y_{1}& y_{2} &y_{3} \end{bmatrix}[/math] Where the top row are labels of each vector while the other values represent the values in each vector. From here, you can do the proper transformations required. This provides information on those concepts: http://www.mathplanet.com/education/geometry/transformations/transformation-using-matrices

Wisdom from a wise man.

As my statement pointed out, there is a group of conservatives who believe that ssm should be legally allowed and some who believe it shouldn't be. I am the former(though my concerns deal with more of the implications than anything that the ruling has on federal over state rulings and what it means for institutions provision of service). Labels help people to determine who to blame in circumstances. Although unrelated, the GamerGate movement was something that was to be identified as a diverse group of beliefs that had one similar idea. However, they got swept under one generalization. Again, it is a sweeping generalization to say that all conservatives are one thing when there are splits in groups.

You know that a thread is over when we can only make jokes to represent how ridiculous an idea is.

*sigh* Thank you for making a sweeping generalization about a particular group. It certainly helps.

http://blogs.wsj.com/digits/2015/06/26/artificial-intelligence-machine-gets-testy-with-its-programmers/ For some reason, a part of this conversation seems like it would come from the Hitchhiker's Guide to the Galaxy series.

Before learning integrals, I think you should start with derivatives first. If that is confusing, I would start with limits of functions then.

I wonder how many times this topic will keep popping up, considering how many times it has been brought up on many other forums. Can't people just accept you can't divide by 0?

What about it do you not understand?

It means that you are taking the reverse derivative of an equation with respect to a particular variable. For example, let's say you have ax+b and the point is to integrat this equation with respect to x, or apply the integral to that particular variable. You would treat every other variable like a constant and simply integrate x. ax^2/2 + bx

What do you mean what is d and what is t? That is part of integral notation. EDIT: I thumbed up the wrong post. I meant just to thumb up ajb. Oops?

I think, in the secular context, it should be constitutional. To be honest, I had my original opinion(that it shouldn't be allowed) of it formed by parental upbringing. I originally thought it was conducted within a religious church and that the decision would force such an action, even when against the will of the religious church. While it can be, in the sense to satisfy the spouses involved, I figured out that it was conducted on a secular level. My original opinion of it was formed by ignorance from upbringing.

I guess we can assume any axiom in any case, but I thought we were talking about real math. EDIT: By real math I am talking about the general axioms that are accepted. If you want to discuss newly made axioms, I think you should read up on axioms and what is considered a consistent axiom. Developing axioms that are inconsistent doesn't form formal mathematical structures. I guess you can try it, out of curiosity, but you might as well be standing in the middle of no where because that is where axioms that are inconsistent will most likely lead you. However, don't let my banter stop you. It might be interesting(or not).

The analogy is completely off. Multiplication is seen as grouping subsets of a particular object that have n amount of that particular object. Let's take your example. We will define a subset A that contains 5 objects called apple. Now, in this case, we want to know the amount of apples if we have B subsets of 5 apples. There, the cardinality of the set of groups of apples will be B. A * 5 = {{apple,apple,apple,apple,apple},{apple,apple,apple,apple,apple},{apple,apple,apple,apple,apple},{apple,apple,apple,apple,apple},{apple,apple,apple,apple,apple}} In this case, we have a total of 25 objects called apple in the set A*B. Now, let's consider what would happen if we multiplied by zero: A*0 = {} We have nothing in the set. Now imagine if we did not know the cardinality of A. A * 0 = {} In this case of multiplication, we know that there are zero subsets, therefore it is trivial. However, look as I do division with A*B. A*B / 0 = {{apple,apple,apple...},{apple,apple,apple...},{apple,apple,apple...}....} It is an undefinable set because you literally can't tell how many apples we started out with our how many subsets of apples we had in the whole set in the first place. Therefore, it is undefinable.(I think this is right).

But isn't the point of a variable to be a representation of a numerical value?

Well, let's test it out. n/0 = n n/0 * 1/n = n * 1/n (n*1)/(0*n) = 1 Because of the order of operations(PEMDAS), the following would have to occur: n/0 = 1 And the original: n/0 = n As you can see here, you would have an inconsistency because n could be any number and the result will always be 1. So, it could equal both n and 1. It could make sense for a parabolic function, but in this context it makes no sense at all. EDIT: Scratch that, it wouldn't make sense for even a parabolic function because for each y value, the x would be a different value.

If there are multiple solutions in this context, then it is an inconsistency within mathematics. if n/0 equals 0, but n can be any value, then it would be an inconsistency.

One of many reasons why division by 0 is undefined is due to the following reason: Let a equal some number and the following be true: a*0 = 0 Now, let's assume we had a variable b, some constant, and the following is true: a/b = c If we set b = 0, the problem would be that we could have multiple solutions for a, if we tried to solve for it. a/0 = c. a could be 1, 2, 3, or any number for that matter. That is one of the reasons why it is undefined. EDIT: I think this article explains it better https://en.wikipedia.org/wiki/Division_by_zero.

I think the revolutionary part of the product comes from the speed and efficiency of the product. I'm not denying that there have been previous products that the intention of doing the same thing. So be it, but we shall see soon. I'm not really concerned about someone's opinion on the novelty of the product, rather I am concerned with the benefits of the product itself and how it will save lives, as it claims. I am going to assume they have work to show for the product. If they don't, then we continue on. http://reference.medscape.com/drugs/hemostatics Here is information about hemostatics. Whether they do happen, the point is they can and have a likelyhood of occurring. Tell me if this reference is viable or not.