What the infinity symbol means
The infinity sign ∞ stands for something without end. In math it is not a number but an idea: a quantity that grows without limit. You will see it in limits (x → ∞), in intervals such as (−∞, ∞), which covers all real numbers, and in sums with infinitely many terms.
The English mathematician John Wallis introduced the sign in 1655. Its sideways figure-eight shape is called a lemniscate, from the Latin word for a ribbon. Set theory goes further and compares sizes of infinity: the natural numbers form the smallest infinite size, written ℵ₀ (aleph-null).
Outside math, ∞ means forever: infinite love, lifelong friendship, eternity. It is a popular choice for tattoos, couple bios and friendship symbols, and a rainbow-colored infinity is widely used as a symbol of neurodiversity.
∞ vs ♾︎
∞ is the math character. It shows up as plain text in any font, takes the color of the surrounding text, and is the one to use in equations. ♾︎ started out as the "permanent paper sign" that marks long-lasting, acid-free paper. Since 2018, phones show it as the ♾️ infinity emoji, which suits chats and social posts better.
Do not confuse ∞ with ∝ (proportional to), which looks like an infinity sign with one side cut open, or with ꝏ, a rare Latin letter.
How to type the infinity symbol
On a Mac, press Option + 5. On Windows, hold Alt and type 236 on the number pad. In Microsoft Word, type 221E and press Alt + X. In Google Docs, use Insert > Special characters and search for "infinity".
On iPhone and Android, open the emoji keyboard and search for "infinity" to get ♾︎. In LaTeX, write \infty. In HTML, use ∞. More signs like this are on the math symbols page.