The Mathematical Symbol "Square Cup (⊔)"
The "Square Cup" Symbol (⊔)
The ⊔ symbol, referred to as the "Square Cup" or "Square Union", is a mathematical notation often used in set theory and boolean algebra. It represents the union operation for two sets, especially when dealing with non-disjoint sets.
Understanding the Square Union
Traditionally, the simple union operation, represented by the "U" symbol, combines elements from two sets without duplication. However, in contexts where repetitions are allowed or multisets are being considered, the square union (⊔) can be used to emphasize that elements can appear multiple times in the resulting set.
Usage in Mathematics
While the square union symbol is less common than the standard union symbol, it's prevalent in specific contexts:
- Set Theory: When considering multisets or bags, where elements can have multiplicity greater than one.
- Boolean Algebra: In certain contexts where the union operation behaves differently.
Examples
Given two multisets A = {1, 1, 2} and B = {1, 2, 2}, the square union would be A ⊔ B = {1, 1, 1, 2, 2, 2}.
Notation
When denoting the square union of two sets, it's common to place the ⊔ symbol between them, similar to the standard union. For instance, A ⊔ B represents the square union of sets A and B.
Conclusion
The ⊔ symbol offers a nuanced approach to the union operation in contexts where repetitions are considered. Though not as commonly used as the standard union, it plays a vital role in certain mathematical areas, providing clarity and specificity in its application.
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Codes for the ⊔ Symbol
| The Symbol | ⊔ | |
| Alt Code | Alt 8852 | |
| HTML Code | ⊔ | |
| HTML Entity | ⊔ | |
| CSS Code | \2294 | |
| Hex Code | ⊔ | |
| Unicode | U+2294 |
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 8852. 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: "\2294";} </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+2294. 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 |
|---|---|
| 2294 [Hold down Alt] [Press x] | ⊔ (The 2294 turns into ⊔. Note that you can omit any leading zeros.) |
| JavaScript Text | Output |
|---|---|
| let str = "\u2294" document.write("My symbol: " + str) | My symbol: ⊔ |