Identical To

The Mathematical Symbol "Identical To (≡)"

The ≡ Symbol in Mathematics: Identical To

Mathematics boasts an extensive array of symbols, each carrying its distinct significance. Among them, the ≡ or "Identical To" symbol plays a pivotal role. This article aims to demystify its meaning, pinpoint its main applications, and provide illustrative examples.

Usage

The ≡ symbol is primarily used to indicate that two expressions are identical in value or form, meaning they are essentially the same in every conceivable way. It goes beyond mere equality by implying a deeper congruence between the two entities.

Examples

• Example 1: In modular arithmetic:
  If two integers \( a \) and \( b \) leave the same remainder when divided by an integer \( n \), we can say \( a ≡ b \) (mod \( n \)). This denotes that \( a \) and \( b \) are identical with respect to modulo \( n \).
• Example 2: In logical equivalences:
  If two logical statements \( P \) and \( Q \) are always true at the same time and always false at the same time, then they are said to be logically equivalent, represented as \( P ≡ Q \).

In summary, the ≡ symbol serves as a powerful notation to express deep congruence or identity between mathematical entities. Recognizing and understanding its implications are crucial for various mathematical theories and proofs.

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Codes for the ≡ Symbol

The Symbol	≡	copy
Alt Code	Alt 8801	copy
HTML Code	≡	copy
HTML Entity	≡	copy
CSS Code	\2261	copy
Hex Code	≡	copy
Unicode	U+2261	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 8801. 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: &#8801;</b>	My symbol: ≡

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

HTML Text	Output
<b>My symbol: &equiv;</b>	My symbol: ≡

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

CSS and HTML Text	Output
<style> span:after { content: "\2261";} </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: &#x2261;</b>	My symbol: ≡

On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x2261 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+2261. 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
2261 [Hold down Alt] [Press x]	≡ (The 2261 turns into ≡. Note that you can omit any leading zeros.)

In JavaScript, the syntax is \uXXXX. So, our example would be \u2261. (Note that the format is 4 hexadecimal characters.)

JavaScript Text	Output
let str = "\u2261" document.write("My symbol: " + str)	My symbol: ≡

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