The same shape one way up and the other, for opposite operations.
Union is the cup, opening upward, and gives everything in either set. Intersection is the cap, opening downward, and gives only what is in both. The spoken names 'cup' and 'cap' exist precisely because the drawings are so easily reversed — reading a formula aloud disambiguates it in a way looking at it does not.
Vertical reflection is the entire difference between them.
Drawn from the visual attributes recorded for each symbol. Only traits the two records disagree about are listed.
| Trait | Intersection sign | Union sign |
|---|---|---|
| Orientation | inverted | upright |
| Intersection sign | Union sign | |
|---|---|---|
| What it gives | Only what is in both sets | Everything in either set |
| Which way it opens | Downward — an arch | Upward — a cup |
| Spoken as | Cap | Cup |
| Result size | Never larger than the smaller set | Never smaller than the larger set |
| Relationship (from Symbolwise's records) | Commonly confused with Union sign — Vertical reflection is the entire difference between them.; Opposite of Union sign — Everything in both sets, against everything in either. | Commonly confused with Intersection sign — The same shape inverted; which way up it sits is the whole distinction.; Opposite of Intersection sign — Everything in either set, against everything in both. |
Unicode Code Chart: Mathematical Operators (U+2200–U+22FF)
The Unicode Consortium · retrieved 2026-07-30
Authoritative for the character's code point, name and block only. Unicode assigns identity; it does not define what a symbol means in use.
Wikipedia · retrieved 2026-07-31
Tertiary reference. Used for what the notation means in ordinary mathematical practice and for attribution of its introduction, not for a claim that any body defines it.
Glossary of mathematical symbols
Wikipedia · retrieved 2026-07-31
Tertiary reference. Used for what the notation means in ordinary mathematical practice and for attribution of its introduction, not for a claim that any body defines it.
Alpha is a Greek letter and stands for a quantity — an angle, a coefficient, a significance level. The proportionality sign is an operator and stands between two quantities to say they keep a constant ratio. The drawings differ in that the proportionality sign's right-hand stroke runs out in an open curve rather than closing into the letter's tail.
Look at the left-hand edge. A straight flat back is an AND gate: the output is true only when every input is. A curved concave back is an OR gate: true when any input is. Everything else about the shapes is similar, which is why the back edge is worth checking deliberately rather than at a glance.
Look at what follows. A prefix never stands alone — it is glued to a unit symbol, as in kW or kg. A constant stands by itself in an equation. Careful physical writing subscripts the constant as k_B for exactly this reason, and the kelvin's capital K is a third claimant to the same letter.
Length is the tell. A crescendo hairpin is drawn long, below a stave, and spans the passage it applies to — its extent *is* the instruction. A less-than sign is one character wide and sits between two values. If it stretches, it is music; if it fits between two numbers, it is mathematics.