Union

The Mathematical Symbol "Union (∪)"

The ∪ Symbol in Mathematics: Representing Union

Within the extensive realm of mathematical symbols, the ∪ symbol stands out as a fundamental representation for the concept of "Union" in set theory. It signifies the combination of two sets, encompassing all distinct elements from both sets. This article delves into the primary uses of the ∪ symbol, accompanied by illustrative examples.

Usage

In set theory, the ∪ symbol is used to show the union of two sets, resulting in a new set that contains all the elements from both constituent sets. If an element belongs to either one of the sets (or both), it will belong to their union.

Examples

• Example 1: Let's consider two sets \( A = \{1, 2, 3\} \) and \( B = \{3, 4, 5\} \). The union of these sets can be expressed as:
  \( A ∪ B = \{1, 2, 3, 4, 5\} \).
• Example 2: For two sets \( X = \{apple, banana\} \) and \( Y = \{banana, cherry, date\} \), their union is:
  \( X ∪ Y = \{apple, banana, cherry, date\} \).

To wrap up, the ∪ symbol holds paramount importance in set theory, enabling mathematicians to express the union of sets succinctly. Its utility extends beyond simple sets, also finding applications in more complex mathematical structures and concepts, such as topological spaces and algebraic structures.

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Codes for the ∪ Symbol

The Symbol	∪	copy
Alt Code	Alt 8746	copy
HTML Code	∪	copy
HTML Entity	∪	copy
CSS Code	\222A	copy
Hex Code	∪	copy
Unicode	U+222A	copy

How To Insert the ∪ Symbol

(Method 1) Copy and paste the symbol.

The easiest way to get the ∪ symbol is to copy and paste it into your document.

Bear in mind that this is a UTF-8 encoded character. It must be encoded as UTF-8 at all stages (copying, replacing, editing, pasting), otherwise it will render as random characters or the dreaded �.

(Method 2) Use the "Alt Code."

If you have a keyboard with a numeric pad, you can use this method. Simply hold down the Alt key and type 8746. When you lift the Alt key, the symbol appears. ("Num Lock" must be on.)

(Method 3) Use the HTML Decimal Code (for webpages).

HTML Text	Output
<b>My symbol: &#8746;</b>	My symbol: ∪

(Method 4) Use the HTML Entity Code (for webpages).

HTML Text	Output
<b>My symbol: &cup;</b>	My symbol: ∪

(Method 5) Use the CSS Code (for webpages).

CSS and HTML Text	Output
<style> span:after { content: "\222A";} </style> <span>My symbol:</span>	My symbol: ∪

(Method 6) Use the HTML Hex Code (for webpages and HTML canvas).

HTML Text	Output
<b>My symbol: &#x222A;</b>	My symbol: ∪

On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x222A to place the ∪ symbol on your canvas. For example:

JavaScript Text
const x = "0x"+"E9" ctx.fillText(String.fromCodePoint(x), 5, 5);
Output
∪

(Method 7) Use the Unicode (for various, e.g. Microsoft Office, JavaScript, Perl).

The Unicode for ∪ is U+222A. The important part is the hexadecimal number after the U+, which is used in various formats. For example, in Microsoft Office applications (e.g. Word, PowerPoint), do the following:

Type	Output
222A [Hold down Alt] [Press x]	∪ (The 222A turns into ∪. Note that you can omit any leading zeros.)

In JavaScript, the syntax is \uXXXX. So, our example would be \u222A. (Note that the format is 4 hexadecimal characters.)

JavaScript Text	Output
let str = "\u222A" document.write("My symbol: " + str)	My symbol: ∪

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