Unitless Unity

Long back I had read a book on Mathematics which talked about numbers. It said that the whole concept of numbers is vague as none of the things which exist are the same (consider the leaves of a tree, every leaf is different from the other). So if two things cannot be same how can you add them and get the sum as twice of any one (for instance, 1+1=2). The theory was pretty neat but somewhere deep down I could not agree. Today, when I think about the same theory, ideas rush into my mind. I say if a leaf of a tree is different from the other (maybe in size, shape, color or something else), this only means that every leaf of a tree has something unique. What about quantifying this uniqueness? If I add two unique items, I can very well get 2 unique items. This is true enough for the human beings as well, we are all different and have a specialty of our own. 2 human beings cannot be added, but there uniqueness / specialty can be added to form a team. So, we are talking UNITY here but the UNIT does not exist. Funny :)