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Today, We are going to discuss a most fundamental concept of mathematics, of course, as well as of probability theory. It is set.

Today, we are going to talk about numbers, especially binary numbers. We had already had abilities to use numbers even when we were babies; for example, you must had asked your mother for ‘an’ apple , ‘a’ toy or ‘one’ dollar. These words are so normal for everyone that, for a long time, we have never recognize that there is an important and essential mathematic concept behind it. That is number. Sure enough, though we all have known $1,2,3,\dots$ very well, what is a number might never have been thought by us untill we were asked to do that. For we will learn to use binary numbers and decimal numbers simultaneously, during which the concept of number is a key point, we have to go closer to the defination of the number.
From now on, assuming that we know nothing about numbers is necessary to make everything clear, during which even $1,2,3,\dots$ are unknown until they are defined formally and precisely.

It had been said that the more basic the operations are, the more we can stand to gain by doing it efficiently. Addition and multiplication may be the most basic operations to us all, and so is their combination, the polynomials. Many functions, however, complicated they are, can be approximated by a polynomial. For instance: $\sin(x),x\in[-\pi,\pi]$ can be approximated by