What is the element-of symbol and how is it used? – TechTarget Definition (2024)

What is element-of symbol?

The element-of symbol is used in mathematical set theory to indicate that a point, object or number belongs to a certain set. The symbol resembles the lowercase Greek letter epsilon, but stretched out (∈). The symbol is read as "is an element of," "is a member of," "is in" or "belongs to." The symbol is sometimes referred to as the "member of" symbol or "belongs to" symbol.

What is the element-of symbol and how is it used? – TechTarget Definition (2)

In mathematics, a set is a collection of objects. The objects might be numbers, letters, variables, symbols, points on a line or other types of objects. Each object that belongs to a set is known as an element or member of that set. For example, a set named A might contain the first five positive integers: 1, 2, 3, 4 and 5. These numbers are the set's elements. Another set, B, might contain the last five lowercase letters in the English alphabet: v, w, x, y and z. In this case, the letters are the elements in set B.

A set such as A is commonly written as follows:

A = {1, 2, 3, 4, 5}

The set members are enclosed in curly braces and separated with commas, all of which are preceded by the A and equal sign. This format works the same way for set B:

B = {v, w, x, y, z}

For either set, the element-of symbol can be used to indicate that an object belongs to that set. For instance, the following expression shows how 3 is related to set A:

3 ∈ A

The expression can be read as "3 is an element of set A," "3 is a member of set A," "3 is in set A" or "3 belongs to set A." We can use the same approach to show how w is related to set B:

w ∈ B

In this case, the expression can be read as "w is an element of set B," "w is a member of set B," "w is in set B" or "w belongs to set B."

When an object does not belong to a set, we can use the not-element-of symbol in much the same way as the element-of symbol. The not-element-of symbol looks like the element-of symbol except that a forward slash runs through it (∉). The not-element-of symbol is read as "is not an element of," "is not a member of," "is not in" or "does not belong to." For example, the following expression indicates that 7 is not an element of set A:

7 ∉ A

The expression can also be read as "7 is not a member of set A," "7 is not in set A" or "7 does not belong to set A." Because 7 is not one of the first five positive integers, it is clearly not part of the set.

Learn about binary and hexadecimal numbering.

This was last updated in January 2023

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What is the element-of symbol and how is it used? – TechTarget Definition (2024)

FAQs

What is the element-of symbol and how is it used? – TechTarget Definition? ›

The element-of symbol is used in mathematical set theory to indicate that a point, object or number belongs to a certain set. The symbol resembles the lowercase Greek letter epsilon, but stretched out (∈).

What is the definition of element and symbol? ›

Symbol of an element is a one or two letter notation that is used for denoting the chemical element. Each element has its own particular symbol. For example, carbon is denoted by the symbol C, sodium by Na, Potassium by K, chlorine by Cl.

What does this mean ∈? ›

The symbol ∈ indicates set membership and means “is an element of” so that the statement x∈A means that x is an element of the set A. In other words, x is one of the objects in the collection of (possibly many) objects in the set A.

What is the simple definition of an element? ›

(EH-leh-ment) A basic part of a whole. In chemistry, refers to a simple substance that cannot be broken down into smaller parts or changed into another substance. The basic part of an element is an atom, which contains protons, neutrons, and electrons. All atoms of an element have the same number of protons.

What is the symbol of an element What information does it contain? ›

The symbol represents a specific element. It only and only represents one atom of an element. It basically represents the number of atoms present in one gram of its atom. It also tells us the amount of heaviness as compared to one atomic mass unit.

What is an element symbol example? ›

Examples of modern element symbols include H for hydrogen, He for helium, and Ca for calcium. The first letter of an element symbol is capitalized, while the second letter is lowercase. An example of a deprecated element symbol is Cb for columbium, the former name of the element niobium, or Nb.

Is an element of symbol meaning? ›

The element-of symbol is used in mathematical set theory to indicate that a point, object or number belongs to a certain set. The symbol resembles the lowercase Greek letter epsilon, but stretched out (∈).

What is the usage of ∈? ›

Denotes set membership, and is read "is in", "belongs to", or "is a member of". That is, means that x is an element of the set S. ∉ Means "is not in".

What does ∈ mean in economics? ›

∈ - this means “in”, that a variable on the left side is contained within a variable, group, or concept on the right side. It can be reversed to mean the opposite. For example, often in economics, a theory will describe which values of x are possible.

What is the ∈ in statistics? ›

ε: “Error term” in regression/statistics; more generally used to denote an arbitrarily small, positive number. ∈ (Variant Epsilon) This version of epsilon is used in set theory to mean “belongs to” or “is in the set of”: x ∈ X; similarly used to indicate the range of a parameter: x ∈ [0, 1].

What is the element in short answer? ›

An element is a substance that cannot be broken down into any other substance. Every element is made up of its own type of atom. This is why the chemical elements are all very different from each other.

What is an element example? ›

Elements are things like oxygen, helium, sodium, hydrogen, gold, carbon, lithium, nitrogen, uranium, copper. Compounds and mixtures like water or stainless steel are not elements. But they are made of elements.

What is the best meaning of element? ›

: any of the fundamental substances that consist of atoms of only one kind and that singly or in combination constitute all matter.

What are elements and symbols? ›

Define Element Symbols and Numbers.

The number of the element is its atomic number, that is the number of protons in the nucleus for every atom of that element. While the element symbol is a one- or two-letter abbreviation of the element's name. It can also refer to an old name. (K, for example, stands for kalium).

What is the element symbol called? ›

Element symbols for chemical elements, also known as atomic symbols, normally consist of one or two letters from the Latin alphabet and are written with the first letter capitalised.

What does a symbol represent? ›

A symbol is a mark, sign, or word that indicates (implies) or is understood as representing an object, idea, or relationship.

What is an element symbol in math example? ›

Mathematics Set Theory Symbols
SymbolSymbol NameExample
a ∈ Belement ofB = {7, 13, 15, 21}, 13 ∈ B
(a, b)ordered pair(1, 2)
x ∉ Anot element ofA = {1, 7, 8, 13, 15, 23}, 5 ∉ A
|B|cardinalityB = {7, 13, 15, 21}, |B|= 4
22 more rows

What is the term symbol of an element? ›

In atomic physics, a term symbol is an abbreviated description of the total spin and orbital angular momentum quantum numbers of the electrons in a multi-electron atom. So while the word symbol suggests otherwise, it represents an actual value of a physical quantity.

What is the of symbol in math? ›

In mathematics, the word "of" is typically represented by the multiplication symbol (×) or an open dot. For example, if you want to express "5 times 3," you can write it as "5 × 3" or "5 · 3."

Do elements have a symbol? ›

Every element in the periodic table is represented by a unique chemical symbol, like O for Oxygen or Mg for Magnesium.

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