So the c function is another function that can be used to create vectors of objects, and you can think of c as standing for concatenate because it can be used to kind of concatenate things together. So, for example, I can create an object called x by concatenating 0.5 and 0.6 and that will give me a numeric vector of lenght 2 for the first element is .5 and the second element is .6. In the second example here, I've got a logical vector, we are concatenating through true and false, so shorthand for true and false, you can use t and f, capital T and capital F, so these 2 lines give you the same objectum, you can create a character vector by concatenating a bunch of characters. You can create integer vector by creating a sequence with colon operator, and you can also create a vector of complex numbers where the i is a special symbol, which indicates the imaginary part of the complex number. So using the vector function you can also create, a vector of a certain type and a certain length. So here, I'm going to create a numeric vector of length 10. And by default it will initialize the vector, with a default value for numeric vectors the default value is zero. So what happens if you take a vect you create a vector and you mix two different types of objects and so the general it that is that r. Will kind of create the least common denominator vector so, will not give you an error but what will happen is that it will coerce the vector to be the, the class that's kind of the least common denominator. So here, in the first example, I've got in trouble concatenating number 1.7 and letter a, so clearly these are not in the same class one is numeric, and the other is character. So the least common denominator here, is going to be character. And so we're, so what you're going to get is that y is going to be a character vector, where the first element is going to be the string 1.7 and the second element's going to be the, the letter A so in the second example here, I've got concatenating true, which is a logical, and a two, which is numeric. And so what's going to happen here is that you're going to get a numeric vector and the true is going to be converted into a number. And so how's that happen, so and the, and by the convention in R true is represented as the number one and false is represented as the number zero. And so what you're going to get here, is a vector 1,2. Lastly this last example here I am calculating the letter A, and the logical true and so here the least common denominator is again going to be character. And so the vector that you end up with is a vector where the first element is A and the second element is the string true, so T R U E. It's not going to be illogical so you need to be a little bit aware, of the types of coercion that can occur in our, when you mix different types of elements in a vector. And because you won't get an error, but, but the coercion will happen behind the scenes. that, in the previous slide we talked about kind of a implicit coercion that occurs behind the scenes, but you can explicitly coerce objects from one class to another using functions that usually start with the word as. So for example, if you want to convert something to a numeric you can use the function called as.numeric. If you want to convert something into character you can use the function as.character now if you apply these functions, so if you apply as.numeric to a numeric vector nothing will happen so, here in this example I'm starting off by creating an object called x which is a sequence of zero to six. So this is going to, this is an integer sequence as you could see when I call class on the object but I convert it into a numeric sequence. And so I can call as.numeric on x, and you can see that it prints out 0, 1, through 6, which look like an integer object but it's actually going to be numeric or I can convert it into a logical and so I can say as.logical on it, and what happens? Well, as you can see, the convention is that 0 is false. And any number that's greater than zero is going to be true so here I've got a, when I convert to logical I get false and then everything else is true when I call as.character on X it takes all the numbers and, and converts them into characters. So now I've got the string zero, the string one, two ect and finally when, if I call as.complex this is fairly straightforward because you can all it does is says that you have a complex number where all the imaginary components are zero, now coercion we'll notice always doesn't work. And when it doesn't work you get what are called NA values. So non sensical coercion will result in NAs. So for example if I take the vector ABC. And call as.numeric. Well there's really no way to convert the letters a, b, and c to numerical variables so what you get is a vector of NAs and plus a warning similarly if you call as.logical on x, you're going to get a vector of NAs The next data type I'm going to talk about is the list. Now I mentioned lists a little bit earlier in this lecture and the idea is that they're, they're like a vector except that every element of a list could be a, an object of a different class and so that makes lists very, very handy for kind of carrying around different types of data. And they're very useful in R and they become very common especially when in conjunction with other types of functions that we're going to learn about. So here I'm creating a list called x by using the list function which is a, which can be used to construct the list. And the first element is a numeric value, numeric object of one. The second element is a character, letter a. Third is illogical and the fourth is a complex number. So this is not a problem with lists and when I autoprint the list you'll see that it prints out a little bit differently It doesn't print out like a vector because every element is different. So you can see that in the double brackets here so the, the elements are indexed by double brackets so the first element is the vector 1. The second element is a vector with A. The third element is a vector with true and the fourth element is a vector. With the complex number 1 + (4i). So lists are indexed you'll notice that el, elements of a list will have double brackets around them elements of other vectors just have the single brackets, so that's one way to separate a list from other types of vectors