In this post we will address what axioms and postulates are. And then we’ll talk about demonstrating results. This principle is fundamental to the development of new mathematics. In simple terms, we can understand it as a sequence of statements, each of which is a consequence of the previous ones or something that we know to be true. How to build something as a consequence of another(s)? Suppose that B is a consequence of previous statements. Of the previous statements, there is a statement A. This way we have:
Every Hunan being has a certain tendency to generalize a thought, for example, if a person has political thoughts contrary to yours, then you are from that political wing. Mainly with the right/left political polarization, but that’s just an example. To avoid controversy, we will present other examples: “All cats are yellow.” “There is at least one green alligator.” These are examples of simple propositions. When we use connectives, problems begin to appear. For example:
An important step in representing statements is using appropriate language. For this we will use letters to make it easier to represent the statements. The first step in this post is to define simple propositions. We define a simple proposition as something that has meaning on its own. For example: “There is a white bear” 10 is greater than 3 Now, an example of a non-simple proposition is “pants”, we have no statement regarding this word.
In pure mathematics what we need to learn is to prove what is proposed. Every mathematician is like Saint Thomas, that is, we have to see it to believe it. However, there is a difference between proving and convincing. What we basically use are writing techniques, more precisely, essay writing (or logical mathematical essay). Any argument that is given to us, when that argument holds water, is usually that this person is trying to convince us that it is true.