The Mathematical Symbol "Set Minus (∖)"

The "Set Minus" Symbol (∖)

The ∖ symbol denotes set subtraction. It visually looks like a backslash and represents the difference between two sets. When you see this symbol, it typically means that elements from one set are being removed from another set.

Visual Representation

The symbol appears as a vertical bar leaning to the right, similar to the common backslash on keyboards, like this: \.

Common Uses

The set minus symbol has distinct applications in set theory:

  • Set Difference: Given two sets \( A \) and \( B \), the expression \( A \setminus B \) refers to the set of all elements in \( A \) that are not in \( B \).
  • Examples:
    • If \( A = \{1, 2, 3, 4\} \) and \( B = \{3, 4, 5\} \), then \( A \setminus B = \{1, 2\} \).
    • If \( X = \{a, b, c\} \) and \( Y = \{b, c, d\} \), then \( X \setminus Y = \{a\} \).

Representation in Other Contexts

In LaTeX, a typesetting system frequently employed for mathematical and scientific documents, the set minus can be represented using the command `\setminus` when in math mode.

Conclusion

The ∖ symbol plays a crucial role in set theory, enabling mathematicians and scholars to define the difference between two sets easily. It simplifies expressions and helps in understanding the relationships and differences between various sets.

Mathematical symbol 'Set Minus'

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Codes for the ∖ Symbol

The Symbol∖
Alt CodeAlt 8726
HTML Code∖
HTML Entity∖
CSS Code\2216
Hex Code∖
UnicodeU+2216

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 8726. When you lift the Alt key, the symbol appears. ("Num Lock" must be on.)

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

HTML TextOutput
<b>My symbol: &#8726;</b>My symbol: ∖

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

HTML TextOutput
<b>My symbol: &setminus;</b>My symbol: ∖

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

CSS and HTML TextOutput
<style>
span:after {
content: "\2216";}
</style>
<span>My symbol:</span> 		My symbol: ∖

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

HTML TextOutput
<b>My symbol: &#x2216;</b>My symbol: ∖
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x2216 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+2216. 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:
TypeOutput
2216
[Hold down Alt]
[Press x]		∖
(The 2216 turns into ∖. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u2216. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u2216"
document.write("My symbol: " + str)		My symbol: ∖