## The Mathematical Symbol "Not Asymptotically Equal To (≄)"

The "Not Asymptotically Equal To" Symbol (≄)

In mathematics, the symbol ≄ represents the non-equivalence of two expressions or values in the context of limits or asymptotic behaviors. Specifically, it denotes that two functions are not asymptotically equivalent.

## Understanding ≄

Two functions \(f(x)\) and \(g(x)\) are said to be asymptotically equivalent if their ratio approaches 1 as \(x\) approaches infinity. When this is not the case, we can use the ≄ symbol to express this non-equivalence.

Example 1: Simple Functions

Let \(f(x) = x^2 + 2x\) and \(g(x) = x^2\). As \(x\) approaches infinity, the ratio \(\frac{f(x)}{g(x)}\) approaches 1, so the two functions are asymptotically equivalent. However, for different functions where the ratio doesn't approach 1, the ≄ symbol would be appropriate.

Example 2: Exponential Growth

Consider \(h(x) = 2^x\) and \(j(x) = x^{10}\). Here, as \(x\) approaches infinity, the growth of \(h(x)\) far outpaces \(j(x)\), so: \[ h(x) ≄ j(x) \]

## Applications of ≄

The ≄ symbol finds its applications in various areas, such as:

**Mathematics:**Especially in analysis and calculus when discussing the behavior of functions at infinity.**Computer Science:**In algorithm analysis, comparing the growth rates of different functions, like time complexities.

In summary, the ≄ symbol is crucial for indicating that two functions do not have the same behavior as they approach infinity or any other specified value.

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## Codes for the ≄ Symbol

The Symbol | ≄ | |

Alt Code | Alt 8772 | |

HTML Code | ≄ | |

HTML Entity | ≄ | |

CSS Code | \2244 | |

Hex Code | ≄ | |

Unicode | U+2244 |

## 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 8772. 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: "\2244";} </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: ≄ |

**0x2244**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+2244**. 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 |
---|---|

2244 [Hold down Alt] [Press x] | ≄ (The 2244 turns into ≄. Note that you can omit any leading zeros.) |

JavaScript Text | Output |
---|---|

let str = "\u2244" document.write("My symbol: " + str) | My symbol: ≄ |