Almost Equal To

The Mathematical Symbol "Almost Equal To (≈)"

The ≈ Symbol in Mathematics: Almost Equal To

The mathematical symbol ≈ stands for "Almost Equal To." Used across various fields of mathematics and science, this notation implies that two values or functions are nearly, but not exactly, equivalent. This article will shed light on two primary contexts where this symbol is typically employed, accompanied by two illustrative examples for each scenario.

1. Analysis and Limits

In the context of calculus and mathematical analysis, the ≈ symbol is used to show that two functions are almost identical, especially as they approach a certain value.

• Example 1: The functions \(f(x) = x^2 + 3x\) and \(g(x) = x^2\) can be said to be almost equal as \(x\) approaches infinity, symbolized as \(f(x) ≈ g(x)\) as \(x \to \infty\).
• Example 2: For large values of \(n\), \(n^3 + 2n^2 + 5n\) and \(n^3\) are almost equal, which can be expressed as \(n^3 + 2n^2 + 5n ≈ n^3\) for large \(n\).

2. Practical Approximations

The ≈ symbol finds a prominent place in practical applications, especially when two measurements or calculations are so close that the difference is negligible for most practical purposes.

• Example 1: If a scientific calculator computes the square root of 3 as approximately 1.73205, we can denote \( \sqrt{3} ≈ 1.732 \).
• Example 2: In physics, if an experimentally derived value for the speed of light is 299,792,457 m/s, it's often rounded to 299,792,458 m/s for convenience. Hence, we might state: Measured speed of light ≈ 299,792,458 m/s.

In essence, the ≈ symbol facilitates the representation of values or functions that are nearly identical in value or behavior, distinguishing between absolute equality and practical equivalence. This notation is indispensable in both pure mathematics and applied sciences.

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Codes for the ≈ Symbol

The Symbol	≈	copy
Alt Code	Alt 8776	copy
HTML Code	≈	copy
HTML Entity	≈	copy
CSS Code	\2248	copy
Hex Code	≈	copy
Unicode	U+2248	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 8776. 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: &#8776;</b>	My symbol: ≈

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

HTML Text	Output
<b>My symbol: &asymp;</b>	My symbol: ≈

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

CSS and HTML Text	Output
<style> span:after { content: "\2248";} </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: &#x2248;</b>	My symbol: ≈

On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x2248 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+2248. 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
2248 [Hold down Alt] [Press x]	≈ (The 2248 turns into ≈. Note that you can omit any leading zeros.)

In JavaScript, the syntax is \uXXXX. So, our example would be \u2248. (Note that the format is 4 hexadecimal characters.)

JavaScript Text	Output
let str = "\u2248" document.write("My symbol: " + str)	My symbol: ≈

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