The Mathematical Symbol "Double Intersection (⋒)"
An Exploration of the "Double Intersection" Symbol (⋒): Insights from Set Theory
In the intricate realm of mathematical notation, certain symbols emerge to encapsulate complex operations in a concise manner. Within set theory, the "Double Intersection", represented by ⋒, is one such pivotal symbol. This article aims to unravel the meaning and applications of this notation, underpinned by clear examples.
Understanding the ⋒ Symbol
The ⋒ symbol, at its essence, pertains to the intersection operation over a collection or family of sets. Unlike the standard intersection symbol that typically concerns the overlap of two sets, the double intersection is employed to represent the intersection of multiple sets, especially when the context involves a family or a sequence of sets.
Example 1:
Suppose we're presented with a family of sets \( \{ C_i \} \) where the index \( i \) runs from 1 to n. To denote the intersection of all these sets, the following notation is used:
⋒ i=1n \( C_i \)
Example 2:
Imagine we have a sequence of sets \( D_j \) defined by some property, for instance, all numbers less than \( j \). If we wish to express the intersection of all these sets for values of \( j \) from 1 to m, the notation becomes:
⋒ j=1m \( D_j \)
The ⋒ notation is common in set theory, particularly when delineating intersections over a defined index set or a broad collection. Grasping this symbol, along with its counterpart for union (⋓), offers a robust foundation for those journeying through the intricacies of set theory and its manifold applications.
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Codes for the ⋒ Symbol
| The Symbol | ⋒ | |
| Alt Code | Alt 8914 | |
| HTML Code | ⋒ | |
| HTML Entity | ⋒ | |
| CSS Code | \22D2 | |
| Hex Code | ⋒ | |
| Unicode | U+22D2 |
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 8914. 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: ⋒</b> | My symbol: ⋒ |
(Method 4) Use the HTML Entity Code (for webpages).
| HTML Text | Output |
|---|---|
| <b>My symbol: ⋒</b> | My symbol: ⋒ |
(Method 5) Use the CSS Code (for webpages).
| CSS and HTML Text | Output |
|---|---|
|
<style> span:after { content: "\22D2";} </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: ⋒</b> | My symbol: ⋒ |
| 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+22D2. 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 |
|---|---|
| 22D2 [Hold down Alt] [Press x] | ⋒ (The 22D2 turns into ⋒. Note that you can omit any leading zeros.) |
| JavaScript Text | Output |
|---|---|
| let str = "\u22D2" document.write("My symbol: " + str) | My symbol: ⋒ |