Short answer: Tap any symbol below to copy it. In Word, turn on Math AutoCorrect and type \in for ∈ or \forall for ∀. Anywhere else, type the hex code and press Alt + X — 2208 then Alt + X gives ∈.
These are the symbols of proofs, discrete maths and formal logic: membership, unions, quantifiers, implication. They’re also the symbols people most often get nearly right — pasting a Greek sigma where a summation belongs, or a Danish Ø where an empty set belongs. There’s a whole section on that below, because it matters more than it sounds. For the everyday operators, see comparison symbols and the full maths collection.
Need something outside maths? The full copy-and-paste symbol keyboard has every mark on one page.
Set theory symbols
| Symbol | Means | Read as | Code point | HTML | Word |
|---|---|---|---|---|---|
| ∈ | is an element of | “x is in A” | U+2208 | ∈ | \in |
| ∉ | is not an element of | “x is not in A” | U+2209 | ∉ | \notin |
| ∋ | contains as member | “A contains x” | U+220B | ∋ | \ni |
| ⊂ | proper subset of | “A is strictly inside B” | U+2282 | ⊂ | \subset |
| ⊆ | subset of or equal to | “A is inside or equals B” | U+2286 | ⊆ | \subseteq |
| ⊄ | not a subset of | U+2284 | ⊄ | \nsubset | |
| ⊃ | proper superset of | U+2283 | ⊃ | \supset | |
| ⊇ | superset of or equal to | U+2287 | ⊇ | \supseteq | |
| ∪ | union | “A or B” | U+222A | ∪ | \cup |
| ∩ | intersection | “A and B” | U+2229 | ∩ | \cap |
| ∖ | set difference | “A without B” | U+2216 | ∖ | \setminus |
| ∅ | empty set | “the set with nothing in it” | U+2205 | ∅ | \emptyset |
| × | Cartesian product | “all pairs from A and B” | U+00D7 | × | \times |
Number sets use double-struck (blackboard bold) capitals:
| Symbol | Set | Code point | HTML |
|---|---|---|---|
| ℕ | natural numbers | U+2115 | ℕ |
| ℤ | integers | U+2124 | ℤ |
| ℚ | rationals | U+211A | ℚ |
| ℝ | reals | U+211D | ℝ |
| ℂ | complex numbers | U+2102 | ℂ |
| ℵ | aleph (cardinality) | U+2135 | ℵ |
These are real characters, not a bold font applied to N and Z. That distinction matters: a bolded N in a Word document is still the letter N to a search index or a screen reader, whereas ℕ is unambiguously the naturals. Use the character.
Logic symbols
| Symbol | Means | Read as | Code point | HTML | Word |
|---|---|---|---|---|---|
| ∀ | universal quantifier | “for all” | U+2200 | ∀ | \forall |
| ∃ | existential quantifier | “there exists” | U+2203 | ∃ | \exists |
| ∄ | there does not exist | “there is no” | U+2204 | ∄ | \nexists |
| ∧ | logical and | “and” | U+2227 | ∧ | \wedge |
| ∨ | logical or | “or” | U+2228 | ∨ | \vee |
| ¬ | negation | “not” | U+00AC | ¬ | \neg |
| ⇒ | implies | “if… then” | U+21D2 | ⇒ | \Rightarrow |
| ⇔ | if and only if | “iff” | U+21D4 | ⇔ | \Leftrightarrow |
| ∴ | therefore | U+2234 | ∴ | \therefore | |
| ∵ | because | U+2235 | ∵ | \because | |
| ⊤ | tautology, true | “top” | U+22A4 | ⊤ | \top |
| ⊥ | contradiction, false | “bottom” | U+22A5 | ⊥ | \bot |
| ⊕ | exclusive or | “xor” | U+2295 | ⊕ | \oplus |
A note on ⊤ and ⊥: their official Unicode names are the opposite of how they’re read. U+22A4 ⊤ is named “down tack” but is read “top”; U+22A5 ⊥ is “up tack” but read “bottom”. Search a character picker for the reading and you’ll find nothing — search the tack name and it appears immediately.
The lookalikes — get these right
Four pairs cause most of the broken maths on the web. In each case the two characters look nearly identical and are completely different code points, so text search fails, screen readers say the wrong thing, and copy-paste into a maths tool breaks.
∑ is not Σ. The summation operator ∑ is U+2211 (N-ary Summation). The Greek capital sigma Σ is U+03A3. They render similarly in many fonts and mean entirely different things. Same story with ∏ (U+220F, N-ary Product) and Greek Π (U+03A0). If you’re writing a sum, use the operator; if you’re writing a Greek letter, use the sigma symbol.
∅ is not Ø. The empty set ∅ is U+2205. The Danish and Norwegian letter Ø is U+00D8. There’s also ⌀ (U+2300), the diameter sign used in engineering drawings. Three characters, three meanings, one shape. The empty set is the narrow one, and it’s the only one that belongs in a proof.
∈ is not ε. “Element of” ∈ is U+2208. Greek epsilon ε is U+03B5. The membership symbol was historically derived from epsilon, which is exactly why the confusion persists — but they are not interchangeable, and epsilon has its own life in analysis as a small quantity.
∧ is not ^. Logical and ∧ is U+2227. The caret ^ is U+005E, an ASCII character meaning exponentiation in most notations. Likewise ∨ (U+2228) is not the letter v. In a formal statement, the caret reads as “to the power of” — the opposite of what you meant.
The quick test: if you produced the character by pressing a key on a US keyboard, it’s almost certainly the wrong one. These operators all live well above the ASCII range.
Word and Outlook: Math AutoCorrect
This is the fastest way to type maths in Word, and it’s off by default outside equations.
- File → Options → Proofing → AutoCorrect Options
- Open the Math AutoCorrect tab
- Tick Use Math AutoCorrect rules outside of math regions
- Confirm Replace text as you type is also ticked, then OK
Now typing \forall followed by a space gives ∀, anywhere in the document. The commands are the LaTeX ones — \in, \cup, \subseteq, \Rightarrow — so if you know LaTeX you already know them, and if you don’t, the table above lists each one. Word’s built-in list is large and can’t be extended, but you can add your own replacements on the ordinary AutoCorrect tab.
Two things to expect. Word inserts the symbol in Cambria Math, which can shift the font of what follows — press Ctrl + Space to return to the paragraph’s normal style. And a space is consumed as the trigger, so you may need to delete it.
Excel doesn’t have this option. There’s no “outside math regions” setting, so the workaround is to add the pairs you use to Excel’s ordinary AutoCorrect list, or build characters with =UNICHAR(8712) for ∈.
Alt + X works in Word regardless: type 2208, press Alt + X, get ∈. Note that Word grabs the hex digits immediately before the cursor, so if a letter a–f or a digit precedes your code, put a space first.
Windows, Mac and everywhere else
Windows outside Word: classic Alt codes can’t reach these — Alt + 0NNN only goes to code point 255 and every symbol here except ¬ and × is far above that (see why Alt codes don’t work). Use Character Map, or copy from above. ¬ is the exception: Alt + 0172 works.
Mac: there is no Option shortcut for these symbols; any page listing one has invented it. Use the Character Viewer — Control + Command + Space, then search by the Unicode name (“union”, “for all”, “element of”). For repeated use, add Unicode Hex Input under System Settings → Keyboard → Text Input → Edit → + → Others, then hold Option and type the four-digit hex code.
ChromeOS and Linux: Ctrl + Shift + U, type the hex code, press Enter.
Google Docs: Insert → Special characters, then search by name — or draw the symbol in the sketch box, which works well for ∀ and ∃. Docs has no Math AutoCorrect equivalent, but you can build your own under Tools → Preferences → Substitutions.
Phones: none of these are on the standard keyboards. Copy them, or save the ones you use as text replacements (iPhone: Settings → General → Keyboard → Text Replacement).
In LaTeX, HTML and MathML
In LaTeX, these are the commands in the Word column above — \in, \cup, \forall, \Rightarrow — used inside maths mode. Full treatment in LaTeX math symbols.
In HTML, use the numeric references or paste the character into UTF-8 source:
html
<p>If x ∈ A ∩ B, then x ∈ A ∧ x ∈ B.</p>
<!-- renders: If x ∈ A ∩ B, then x ∈ A ∧ x ∈ B. -->For anything more than an inline symbol, MathML is the accessible option, and browser support is now good:
html
<math>
<mi>x</mi><mo>∈</mo><mi>A</mi>
</math>The accessibility point is worth taking seriously. A screen reader encountering ∈ in plain prose reads its Unicode name — “element of” — which is fine. It reads a bolded capital N as “N”, losing the meaning entirely, and it reads a Greek Σ used as a summation as “sigma”, which is wrong. Using the correct code point is an accessibility decision as much as a typographic one. Background: what Unicode is.
Troubleshooting
| Problem | Fix |
|---|---|
Alt + 0NNN produces nothing | These code points are above 255. Use \command in Word, hex + Alt + X, or copy. ¬ (Alt + 0172) is the only one that works |
\forall isn’t converting in Word | Tick Use Math AutoCorrect rules outside of math regions under File → Options → Proofing → AutoCorrect Options |
| My font changed after inserting a symbol | Word switches to Cambria Math. Press Ctrl + Space to return to normal style |
| Alt + X converted too much | Word takes the hex digits before the cursor. Insert a space before the code, or select just the code |
| The symbol shows as a box | Font coverage — ℵ, ∄ and ⊤ ⊥ are the thinnest. See symbols showing as boxes |
| My ∑ won’t paste into a maths tool | You probably have Greek Σ (U+03A3), not the operator ∑ (U+2211). Copy it from above |
| Searching a picker for “top” finds nothing | ⊤ is officially “down tack”. Search the tack names |
| Math AutoCorrect doesn’t work in Excel | Excel has no outside-math-regions setting. Add the pairs to ordinary AutoCorrect, or use =UNICHAR(8712) |
Which method should you use?
| If you… | Do this |
|---|---|
| Need one symbol now | Copy it from the grid above |
| Write maths in Word regularly | Turn on Math AutoCorrect — biggest single time-saver here |
| Write one symbol in Word | Hex code + Alt + X |
| Are on a Mac | Character Viewer, or add Unicode Hex Input |
| Write papers | LaTeX — see LaTeX math symbols |
| Publish maths on the web | Numeric references inline; MathML for real expressions |
| Are teaching | Copy from here — and see teacher math symbols for the classroom set |
For Greek letters as letters — α β θ λ π σ — see the Greek alphabet guide. For ≈ ≤ ≥ ≠, see comparison symbols.
Frequently asked questions
How do I type the element-of symbol ∈?
In Word with Math AutoCorrect enabled, type \in followed by a space. Otherwise type the hex code 2208 and press Alt + X. On a Mac, open the Character Viewer with Control + Command + Space and search “element of”. On ChromeOS or Linux, press Ctrl + Shift + U, type 2208, then Enter. Or copy it from this page.
What is the difference between ∑ and Σ?
They are different characters. ∑ (U+2211) is the N-ary summation operator used in mathematics. Σ (U+03A3) is the Greek capital letter sigma. They look similar in many fonts but are not interchangeable — using the Greek letter as a summation breaks text search, screen-reader output and maths software.
What is the empty set symbol?
It’s ∅ (U+2205). It is not the Danish letter Ø (U+00D8) and not the diameter sign ⌀ (U+2300), although all three look alike. In LaTeX and Word’s Math AutoCorrect the command is \emptyset.
Is there an Alt code for set theory symbols?
Almost never. Classic Alt + 0NNN codes only reach code points up to 255, and nearly all of these symbols sit above that. The negation sign ¬ is the exception at Alt + 0172. For the rest, use Word’s \command shortcuts, hex plus Alt + X, or copy them.
What is the difference between ⊂ and ⊆?
⊂ means proper subset — A is contained in B and is not equal to B. ⊆ means subset or equal — A is contained in B and may be B itself. Some authors use ⊂ loosely for either, so check the convention of whatever you’re reading.
How do I type ∀ and ∃ on a Mac?
There is no Option key shortcut for them. Open the Character Viewer with Control + Command + Space and search “for all” or “there exists”. For frequent use, add Unicode Hex Input as an input source, then hold Option and type 2200 for ∀ or 2203 for ∃.
Written by Igor R. Tested on Windows 11, macOS, iOS, Android, ChromeOS, Linux, Microsoft Word and Google Docs. Last updated August 2026. Symbol code points follow the Unicode Standard.