They sold their van, and bought a compact car after their children grew up. Colby has a compact build, and is quite strong. These new compact digital cameras can fit in a shirt pocket.

2a : having a dense structure or parts or units closely packed or joined a compact woolen compact bone. b : not diffuse or verbose a compact statement. c : occupying a small volume by reason of efficient use of space a compact camera a compact formation of troops.

A compact is a signed written agreement that binds you to do what you’ve promised. It also refers to something small or closely grouped together, like the row of compact rental cars you see when you wanted a van.

adjective. joined or packed together; closely and firmly united; dense; solid: compact soil. arranged within a relatively small space: a compact shopping center; a compact kitchen. designed to be small in size and economical in operation. solidly or firmly built: the compact body of a lightweight wrestler.

Word forms: compacts A compact person is small but looks strong.

Compact Synonyms – WordHippo Thesaurus….What is another word for compact?

dense	crowded
tight	solid
close	serried
compressed	condensed
compacted	impenetrable

My aunt picked me up in her cramped two-door car. A car that is compact, however, can fit everything you need into just a small space. This word has a positive connotation. A cramped car, on the other hand, conjures images of tightly squeezed passengers and belongings.

Definition. Options. Rating. COMPACT. COMmittee to Preserve American Color Television.

A set S of real numbers is called compact if every sequence in S has a subsequence that converges to an element again contained in S.

So the number line is not compact because we have found an open cover that does not have a finite subcover. A set does not have to be infinite in length or area to be non-compact. A closed interval and an open interval make a good case study for how we can think about compactness.

Lemma 2.1 Let Y be a subspace of topological space X. Then Y is compact if and only if every covering of Y by sets open in X contains a finite subcollection covering Y . Theorem 2.1 A topological space is compact if every open cover by basis elements has a finite subcover.

The set of natural numbers N is not compact. The sequence { n } of natural numbers converges to infinity, and so does every subsequence. But infinity is not part of the natural numbers.

Examples. Any finite topological space, including the empty set, is compact. More generally, any space with a finite topology (only finitely many open sets) is compact; this includes in particular the trivial topology. Any space carrying the cofinite topology is compact.

In the general realm of topology, these concepts are not really too related to each other. For example, in a finite set with the discrete topology every set is compact which are both open and closed. A compact set is not guaranteed to be closed unless you are in a Hausdorff space.

Considered as a subset of the real number line (or more generally any topological space), the empty set is both closed and open. Moreover, the empty set is a compact set by the fact that every finite set is compact. The closure of the empty set is empty.

In mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.

The empty set (∅) has no members. This placeholder is equivalent to the role of “zero” in any number system. Examples of empty sets include: The set of real numbers x such that x2 + 5, The number of dogs sitting the PSAT.

Hence the empty set is a subset of every set. No. A subset of a set is another set that does not contain any elements which are not elements of the set to which it is a subset. The empty set is not an element of {1,2,3}.

The empty set can be an element of a set, but will not necessarily always be an element of a set. E.g. What will be true however is that the empty set is always a subset of (different than being an element of) any other set.

Yes, the set {empty set} is a set with a single element. The single element is the empty set. {empty set} is NOT the same thing as the empty set.

More generally, whenever an ideal is taken as understood, then a null set is any element of that ideal. Whereas an empty set is defined as: In mathematics, and more specifically set theory, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.

In mathematical sets, the null set, also called the empty set, is the set that does not contain anything. It is symbolized or { }. There is only one null set. This is because there is logically only one way that a set can contain nothing.

symbol ∅

Definition: A set is a well-defined collection of distinct objects. The objects of a set are called its elements. If a set has no elements, it is called the empty set and is denoted by ∅. In this notation, the braces { } are used to enclose the objects in the set.

Types of a Set

• Finite Set. A set which contains a definite number of elements is called a finite set.
• Infinite Set. A set which contains infinite number of elements is called an infinite set.
• Subset.
• Proper Subset.
• Universal Set.
• Empty Set or Null Set.
• Singleton Set or Unit Set.
• Equal Set.

Set is defined as a well-defined collection of objects. Different types of sets are classified according to the number of elements they have. Basically, sets are the collection of distinct elements of the same type. For example, a basket of apples, a tea set, a set of real numbers, natural numbers, etc.

Symbol	Meaning	Example
{ }	Set: a collection of elements	{1, 2, 3, 4}
A ∪ B	Union: in A or B (or both)	C ∪ D = {1, 2, 3, 4, 5}
A ∩ B	Intersection: in both A and B	C ∩ D = {3, 4}
A ⊆ B	Subset: every element of A is in B.	{3, 4, 5} ⊆ D

Operations on Sets

Operation	Notation	Meaning
Intersection	A∩B	all elements which are in both A and B
Union	A∪B	all elements which are in either A or B (or both)
Difference	A−B	all elements which are in A but not in B
Complement	ˉA (or AC )	all elements which are not in A