In math, except is written ∖, Set minus, U+2216: A ∖ B is everything in A that is not in B. It is a character of its own, not the backslash key. A web page writes ∖ and LaTeX \setminus.
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Excluding a number or a whole set
ℝ∖{0} is the real numbers excluding zero: the braces make a set of the 0, and ∖ takes that set away. ℝ∖ℚ leaves the irrational numbers. Discrete math, which covers set theory, calls A ∖ B the set difference. The standard ISO 31-11 writes it with ∖; some books write A − B, which can also mean every a − b.
Including and not including an endpoint
For a range, the brackets say it. A square bracket means including the endpoint and a round one not including it: [2,5) runs from 2 up to but not including 5. Another notation turns the bracket outward instead: [2,5[.
x ≠ 0 leaves out a single value with no set notation at all.
A ∖ B is the same set as A ∩ Bᶜ, A cut down to the complement of B.
Questions and answers
What is the math symbol for excluding?
∖, the set minus sign. The set to keep goes on its left and what to exclude on its right: ℤ∖{0} is every integer excluding zero, and {1,2,3}∖{2,3,4} is {1}.
Which symbol means not include in discrete math?
It depends on what is left out. A ∖ B does not include the members of B. x ∉ A says that one thing is not in A. A ⊄ B says that the set A is not wholly inside B.
How do union, intersection and except differ?
A ∪ B, the union, is everything in either set. A ∩ B, the intersection, is what both share. A ∖ B, the except or difference, is what A has and B does not.
Is the except symbol the same as a backslash?
No. The backslash is U+005C, a key on the keyboard; set minus is U+2216, a math operator. LaTeX has both: \setminus draws the stroke of \backslash with a little more space on each side, and the amssymb package adds \smallsetminus.
All 32 signs and strings
Start here 6
A∖BA without BA, U+2216, B: the elements of A that are not in B. Put your own two sets in place of the letters.
ℝ∖{0}All real numbers except zeroℝ, U+2216 and a 0 in braces: every real number except zero. Another number in the braces leaves that one out.
∁ComplementU+2201. Everything that is not in a set: ∁A is the complement of A. ∁ in HTML; \complement in LaTeX needs the amssymb package.
∉Not an element ofU+2209. One thing left out of a set: x ∉ A says that x is not in A. ∉ in HTML, \notin in LaTeX.
≠Not equal toU+2260. Leaves one value out of a condition: x ≠ 0 is every x except 0. Option+= on a U.S. keyboard, ≠ in HTML, \ne in LaTeX.
∖Set minusU+2216. The sign of the set difference: A ∖ B is everything in A except what is also in B. ∖ in HTML, \setminus in LaTeX.
Show all 32 signs and strings (26 more)
Ready to edit 6
ℤ∖{0}All integers except zeroThe same pattern with ℤ: every integer except 0.
U∖AComplement of A in UEverything in the universe U that is not in A: the complement of A written as a difference.
A∩BᶜDifference written as an intersectionThe same set as A ∖ B: what A shares with the complement of B. The raised c is U+1D9C.
ℝ∖ℚThe irrational numbersThe real numbers without the rational ones. What remains is the set of irrationals.
x∉Ax is not in AThe statement that one thing, x, is left out of the set A.
x≠0x is not zeroEvery value of x except 0.
Other signs 5
AᶜComplement of AA with a raised c, U+1D9C: the usual way to write everything that is not in A.
A′Complement of A, with a primeA and the prime, U+2032: another way to write the complement of A.
A−BDifference with a minus signA ∖ B spelled with the minus sign, U+2212, as some books do.
−Minus signU+2212. Some books write the set difference with it, A − B, which can also be read as every a − b; the standard sign is ∖. − in HTML.
⊄Not a subset ofU+2284. A ⊄ B: the set A is not wholly inside B. ⊄ in HTML.
Union and intersection 4
⊖Circled minusU+2296. Unicode's other name for it is symmetric difference: A ⊖ B is the same set as A ∆ B. ⊖ in HTML, \ominus in LaTeX.
∆IncrementU+2206. Unicode lists symmetric difference among its uses: A ∆ B is what is in exactly one of the two sets. Option+J on a U.S. keyboard.
∩IntersectionU+2229. A ∩ B is what the two sets share. Alt+239, ∩ in HTML, \cap in LaTeX.
∪UnionU+222A. A ∪ B is everything that is in A, in B or in both. ∪ in HTML, \cup in LaTeX.
Including or not 5
[a,b]Closed intervalSquare brackets include both endpoints: every number from a to b, a and b among them.
(a,b]Half-open interval, a left outNot including a, up to and including b.
[a,b)Half-open interval, b left outFrom a up to but not including b: a is in, b is not.
[a,b[Interval with a reversed bracketThe same interval as [a,b): a bracket turned outward marks the endpoint that is left out.
(a,b)Open intervalRound brackets leave both endpoints out: the numbers between a and b, not including a or b.
Backslashes 6
⧹Big reverse solidusU+29F9. A taller stroke. Unicode's other name for it is z notation schema hiding.
\Fullwidth reverse solidusU+FF3C. The backslash in its fullwidth form, from the block Halfwidth and Fullwidth Forms.
⟍Mathematical falling diagonalU+27CD. A longer diagonal that Unicode cross-refers to set minus, added in version 6.1 (2012). \diagdown in LaTeX, with the amssymb package.
\Reverse solidusU+005C. The backslash of the keyboard. Unicode cross-refers it to set minus and keeps the two apart. \ in HTML, \backslash in LaTeX.
⧵Reverse solidus operatorU+29F5. A backslash made to be a math operator, in Unicode since version 3.2 (2002).
﹨Small reverse solidusU+FE68. The backslash in a small form, from the block Small Form Variants.