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hello and welcome back to start learning sets and as always i want to thank all the nice people that support this channel on steady or paypal today in part 5 we will continue talking about maps in particular we talk about images and pre images please recall we defined a map as a special relation between two sets and we can write it as an assignment from a into b here we call a the domain of the map f and b the codomain okay so lets look again at an example here the map f should map the natural numbers into the integers and the map is defined by saying that a natural number x should be sent to x squared so here you see this error is what we use for the elements and this error is what we use for the sets or in other words the second line here is simply a new notation we use for f x is equal to x squared now as we have done it in the last video lets look at the visualization of this particular map here so here we have the natural numbers on the left hand side and the integers on the rig