Asymptotically Equal To Symbol
≃ (U+2243) denotes that two quantities become equal in the limit, often at large values.
U+2243
The symbol ≃ is used to express “asymptotic equality,” meaning two expressions match as an argument grows. It appears often in math, physics, and computer science. This page helps you copy the symbol and use it correctly in your writing and code.
Asymptotically Equal To Symbol Meaning
≃ means “asymptotically equal to” (Unicode name: ASYMPTOTICALLY EQUAL TO, U+2243). It indicates that the difference between two quantities becomes negligible in a limiting regime, such as as x → ∞ or as a parameter approaches a particular value. Unlike strict equality (=), ≃ allows approximation: the expressions may not be identical everywhere, but they agree in the asymptotic sense. A common interpretation is that f(x)/g(x) approaches 1 in the relevant limit, or that f(x) and g(x) have the same leading behavior. It’s widely used for approximations, simplifying analysis, and describing growth rates.
Common uses
- •Writing asymptotic approximations in calculus and analysis (large x or small h).
- •Describing algorithm runtime behavior, e.g., comparing observed growth with a theoretical model.
- •Modeling physical systems where dominant terms match at extremes (high energy, large distance).
- •Summarizing leading-order behavior in series expansions without claiming exact equality.
- •Documenting that two formulas have the same limiting behavior for engineering approximations.
Examples
≃ Asymptotically Equal To Symbol (U+2243)
- ≃As x → ∞, x^2 + 3x ≃ x^2.
- ≃sin(x) ≃ x for small x.
- ≃e^x − 1 ≃ e^x when x is large.
- ≃For large n, log(n!) ≃ n log(n) − n.
- ≃Complexity: T(n) ≃ n log n for big n.
Variations
Ready to copy
Technical codes
| Unicode | U+2243 | |
| HTML Entity | ≃ | |
| HTML Code | ≃ | |
| CSS | \2243 | |
| Alt Code | Alt + 8771 | |
| Decimal | 8771 |
How to type Asymptotically Equal To Symbol (≃)
On Windows
Hold Alt and type 8771 on the numeric keypad. In Word, type 2243 then press Alt + X.
On Mac
Switch to the Unicode Hex Input keyboard, then hold Option and type 2243. Or press Control + Command + Space and search.
On Linux
Press Control + Shift + U, type 2243, then press Enter or Space.
Anywhere
Copy ≃ with the button above and paste it wherever you need it — this works on every device and in every app, with no keyboard shortcut to remember.
FAQ
What does ≃ mean in math?
≃ means “asymptotically equal to,” indicating two expressions agree in the limit (often as a variable grows), rather than being exactly equal for all values.
Is ≃ the same as ≈?
Not always. ≈ generally indicates approximate equality, while ≃ specifically emphasizes equality in an asymptotic regime (limit behavior).
How do I type ≃ in code or documents?
You can copy the symbol directly, or use HTML entity ≃, CSS escape \\2243, or JavaScript escape \\u{2243}.
When should I use ≃ instead of =?
Use ≃ when you mean agreement only in a limiting sense (e.g., dominant terms match as x → ∞), not exact equality everywhere.