Totally Bounded Set:. Here, we see about bounded set. It’s a set which consists of both upper. and lower bound values. If a set is said to be totally bounded, then. the set is only bounded. A subset is used to cover the totally bounded set. A totally bounded set contains both the upper and lower bound. . Set theory is an important branch of mathematics. It’s the study of mathematical logic and its applications. Set theory defines a term “set”. A set is defined as the collection of elements, such as numbers or other objects, which are arranged in a group. The set contains the elements of similar type or category. The set with any numbers can be denoted in the symbol braces { } For example, the set of numbers may be represented as {2, 3, 4, 5, 6}. We can also write this set as {x : 1 andlt; x andlt; 7}. A totally bounded set is defined as a set which is having a definite or finite size. The bounded set consists of the numbers which are the set of real numbers. A bounded set has both the upper and lower bounds that exists within a particular interval. The bounded numbers in a set are having a definite or fixed size and it always lies between the given intervals. The bounded set contains a bounded sequence form Set theory basically deals with set and set operations. Though, it includes a quite vast study of logic and reasoning. In this page, we’re going to focus on introduction of set theory, basic formulas used in set theory, some basic properties and introduction to the Venn diagram. Therefore students, go ahead with us and gain knowledge about set theory in this chapter . .