MATHUP Animations

They asked a mathematician how much 2 + 2 would be, and the mathematician thought and said: “If 1 + 1 = 2, 2 + 2 is 4” The first time I heard Russell's word came to mind, the Euclid's 5th postulate. Before we move on to this postulate, let's look at the answer to the question: what is postulate? Every science for proof starts with the assumptions that constitute the principles of its subject. Some of these assumptions are common to all fields of science (Aristotle calls them axioms); others are principles specific to each subject's own subject (Aristotle calls them postulates). Postulates are propositions that determine the objects of study, their properties and relationships. For example, geometry assumes objects such as ‘point’, ‘line,, and other defined objects such as‘ triangle ’and‘ circle, are built on the basis of default objects. For example, the postulate “All right angles are equal getirmek expresses a particular property of a set object. Summaries Axiom is valid for all fields and its accuracy is obvious. For example, eşit Things equal to the same thing are equal to each other. ” Postulate is a specific proposition that is specific to a particular subject or area of ​​study. For example, "There is only one parallel line from any point other than a line to that line." Axiom accuracy is a mandatory proposition; whereas there is no obligation for postulate. (I) In spite of all these distinctions, we have to accept the existence of an understanding that considers axiom and postulate as roughly a “proposition considered unproven” (ii). Now let's go back to the beginning and listen to Euclid. In Euclid's 5th postulate, he says: Orsa If the two straight lines on the same plane both intersect with a third straight line, and if the sum of the inner angles on one side is less than two right angles, then if the sum of the angles is less than two right angles, the two intersect correctly. ” Or as we are more familiar with: ilebilir Only one parallel line can be drawn from a point outside a line. ” Who can object to it so clearly and clearly. Of course, if we expand our perspective, when we look at the events in the wider framework, we see that there are environments in which this postulate is invalid. p: yalnız Only one parallel line can be drawn from a point other than a line. p So when we accept our proposition p, we suddenly find ourselves in Euclidean geometry. But if we change our proposition p, we open the door to brand new geometries. So perhaps we have looked at what Russell means in the broadest window.