MTH104 Official Handouts

In mathematics, a proof is a demonstration that, assuming certain axioms, some statement is necessarily true. That is, proof is a logical argument, not an empirical one. One must demonstrate that a proposition is true in all cases before it is considered a theorem of mathematics. An unproven proposition for which there is some sort of empirical evidence is a conjecture. Mathematical logic is the framework upon which rigorous proofs are built. It is the study of the principles and criteria of valid inference and demonstrations. In set theory, we study sets, which are informally collection of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. A rigorous analysis of set theory belongs to the foundations of analysis of set theory belongs to the foundations of mathematics and mathematical logic. A Set Theorist explores what is provable—and what is not provable— when one is allowed to use all of the usual tools of mathematical constructions and proofs (tools such as: creating A fundamental concept in all branches of mathematics is that of a set. A set is any well-defined list, collection, or class of objects. The objects in sets, as we shall see from our examples, can be anything: numbers, people, letters rivers etc These objects are called the elements letters, rivers, etc. These objects are called the elements or members of the set.