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.