The Mathematical Symbol "Approaches the Limit (≐)"

Understanding the ≐ Symbol in Mathematics: Approaching Limits

The ≐ symbol in mathematics is indicative of a value or function "Approaching a Limit". This notation is central to the field of calculus and is often used to describe the behavior of functions as they get close to a certain point, without necessarily reaching it. This article will delve into two main contexts where this symbol is employed, providing two illustrative examples for each scenario.

1. Limits in Calculus

In calculus, ≐ is commonly used to denote that a function approaches a specific value as its variable approaches another value.

  • Example 1: To express that the function \( f(x) = x^2 \) approaches 4 as \( x \) approaches 2, we can write: \( f(x) ≐ 4 \) as \( x \to 2 \).
  • Example 2: When describing the behavior of the function \( g(t) = \frac{1}{t} \) as \( t \) approaches zero from the positive side, it can be denoted as \( g(t) ≐ \infty \) as \( t \to 0^+ \).

2. Convergence in Series

Within the context of infinite series, the ≐ symbol can describe a series' tendency to converge to a particular value.

  • Example 1: If the infinite series \( \sum_{n=1}^{\infty} \frac{1}{n^2} \) has a sum \( S \), then the partial sums of the series can be represented as \( S_n ≐ S \) as \( n \to \infty \).
  • Example 2: For the geometric series \( \sum_{k=0}^{\infty} \frac{1}{2^k} \) which converges to 2, the series' behavior can be captured as \( S_k ≐ 2 \) as \( k \to \infty \).

In summary, the ≐ symbol is a fundamental notation in mathematics, particularly in calculus and analysis. It captures the essence of functions, sequences, or series approaching a specific value or limit, providing a deeper understanding of their behavior in given contexts.

Mathematical symbol 'Approaches the Limit'

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Codes for the ≐ Symbol

The Symbol
Alt CodeAlt 8784
HTML Code≐
HTML Entity≐
CSS Code\2250
Hex Code≐

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 8784. 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: &#8784;</b>My symbol: ≐

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

HTML TextOutput
<b>My symbol: &esdot;</b>My symbol: ≐

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

CSS and HTML TextOutput
span:after {
content: "\2250";}
<span>My symbol:</span>
My symbol: ≐

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

HTML TextOutput
<b>My symbol: &#x2250;</b>My symbol: ≐
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x2250 to place the ≐ symbol on your canvas. For example:
JavaScript Text
const x = "0x"+"E9"
ctx.fillText(String.fromCodePoint(x), 5, 5);

(Method 7) Use the Unicode (for various, e.g. Microsoft Office, JavaScript, Perl).

The Unicode for ≐ is U+2250. 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:
[Hold down Alt]
[Press x]

(The 2250 turns into ≐. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u2250. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u2250"
document.write("My symbol: " + str)
My symbol: ≐