Equivalent To

The Mathematical Symbol "Equivalent To (≍)"

The ≍ Symbol in Mathematics: Equivalent To

The extensive realm of mathematical notation is replete with symbols, each carrying a distinct significance. Among these, the ≍ symbol, denoting "Equivalent To", plays a pivotal role in various branches of mathematics. This article delves into its meaning, supplemented by apt examples.

Usage

The ≍ symbol represents a strong form of equivalence between two mathematical statements or entities, suggesting that they can be used interchangeably in any context without any change in truth value or meaning.

Examples

• Example 1: In logic and boolean algebra, two boolean expressions might be found to have the same truth table. For instance, given the expressions \( P \) and \( Q \), if they always yield the same truth values, one might state:
  \( P ≍ Q \)
  This implies that \( P \) is equivalent to \( Q \) in terms of their truth values.
• Example 2: In mathematics, especially when working with functions or equations, two expressions might yield the same results for all input values. If \( f(x) \) and \( g(x) \) produce the same output for every \( x \), it can be expressed as:
  \( f(x) ≍ g(x) \)
  This signifies that the functions are equivalent across their entire domains.

In essence, the ≍ symbol offers a robust way to convey equivalence in various mathematical contexts, asserting the interchangeability of two entities or statements without any loss of meaning or truth. Its use is vital for highlighting such strong equivalences, fostering clarity in mathematical discussions.

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Codes for the ≍ Symbol

The Symbol	≍	copy
Alt Code	Alt 8781	copy
HTML Code	≍	copy
HTML Entity	≍	copy
CSS Code	\224D	copy
Hex Code	≍	copy
Unicode	U+224D	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 8781. 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: &#8781;</b>	My symbol: ≍

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

HTML Text	Output
<b>My symbol: &asympeq;</b>	My symbol: ≍

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

CSS and HTML Text	Output
<style> span:after { content: "\224D";} </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: &#x224D;</b>	My symbol: ≍

On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x224D 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+224D. 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
224D [Hold down Alt] [Press x]	≍ (The 224D turns into ≍. Note that you can omit any leading zeros.)

In JavaScript, the syntax is \uXXXX. So, our example would be \u224D. (Note that the format is 4 hexadecimal characters.)

JavaScript Text	Output
let str = "\u224D" document.write("My symbol: " + str)	My symbol: ≍

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