DLMF:26.18.E1 (Q7984): Difference between revisions

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‎Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q11965 / rank
 
Normal rank
Property / Symbols used: Q11965 / qualifier
 
Defining formula:

∩ {\displaystyle{\displaystyle\cap}}

\cap
Property / Symbols used: Q11965 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r27.m2adec
Property / Symbols used
 
Property / Symbols used: Q10785 / rank
 
Normal rank
Property / Symbols used: Q10785 / qualifier
 
Defining formula:

∖ {\displaystyle{\displaystyle\setminus}}

\setminus
Property / Symbols used: Q10785 / qualifier
 
xml-id: introduction.Sx4.p2.t1.r19.m2adec
Property / Symbols used
 
Property / Symbols used: Q10824 / rank
 
Normal rank
Property / Symbols used: Q10824 / qualifier
 
Defining formula:

∪ {\displaystyle{\displaystyle\cup}}

\cup
Property / Symbols used: Q10824 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r28.m2adec
Property / Symbols used
 
Property / Symbols used: Q12176 / rank
 
Normal rank
Property / Symbols used: Q12176 / qualifier
 
Defining formula:

j 𝑗 {\displaystyle{\displaystyle j}}

j
Property / Symbols used: Q12176 / qualifier
 
xml-id: C26.S1.XMD3.m1dec
Property / Symbols used
 
Property / Symbols used: Q12172 / rank
 
Normal rank
Property / Symbols used: Q12172 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12172 / qualifier
 
xml-id: C26.S1.XMD6.m1dec
Property / Symbols used
 
Property / Symbols used: Q12228 / rank
 
Normal rank
Property / Symbols used: Q12228 / qualifier
 
Defining formula:

A k subscript 𝐴 𝑘 {\displaystyle{\displaystyle A_{k}}}

A_{k}
Property / Symbols used: Q12228 / qualifier
 
xml-id: C26.S18.XMD1.m1dec
Property / Symbols used
 
Property / Symbols used: Q12229 / rank
 
Normal rank
Property / Symbols used: Q12229 / qualifier
 
Defining formula:

S 𝑆 {\displaystyle{\displaystyle S}}

S
Property / Symbols used: Q12229 / qualifier
 
xml-id: C26.S18.XMD2.m1dec

Latest revision as of 14:12, 2 January 2020

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DLMF:26.18.E1
No description defined

    Statements

    Defining formula
    | S ∖ ( A 1 ∪ A 2 ∪ ⋯ ∪ A n ) | = | S | + ∑ t = 1 n ( - 1 ) t ⁢ ∑ 1 ≤ j 1 < j 2 < ⋯ < j t ≤ n | A j 1 ∩ A j 2 ∩ ⋯ ∩ A j t | . 𝑆 subscript 𝐴 1 subscript 𝐴 2 ⋯ subscript 𝐴 𝑛 𝑆 superscript subscript 𝑡 1 𝑛 superscript 1 𝑡 subscript 1 subscript 𝑗 1 subscript 𝑗 2 ⋯ subscript 𝑗 𝑡 𝑛 subscript 𝐴 subscript 𝑗 1 subscript 𝐴 subscript 𝑗 2 ⋯ subscript 𝐴 subscript 𝑗 𝑡 {\displaystyle{\displaystyle\left|S\setminus(A_{1}\cup A_{2}\cup\cdots\cup A_{% n})\right|=\left|S\right|+\sum_{t=1}^{n}(-1)^{t}\sum_{1\leq j_{1}<j_{2}<\cdots% <j_{t}\leq n}\left|A_{j_{1}}\cap A_{j_{2}}\cap\cdots\cap A_{j_{t}}\right|.}}
    0 references
    DLMF id
    DLMF:26.18.E1
    0 references
    Symbols used
    Q12227
    Defining formula
    | A | 𝐴 {\displaystyle{\displaystyle\left|\NVar{A}\right|}}
    xml-id
    C26.S1.p2.t1.r5.m3adec
    0 references
    Q11965
    Defining formula
    ∩ {\displaystyle{\displaystyle\cap}}
    xml-id
    introduction.Sx4.p1.t1.r27.m2adec
    0 references
    Q10785
    Defining formula
    ∖ {\displaystyle{\displaystyle\setminus}}
    xml-id
    introduction.Sx4.p2.t1.r19.m2adec
    0 references
    Q10824
    Defining formula
    ∪ {\displaystyle{\displaystyle\cup}}
    xml-id
    introduction.Sx4.p1.t1.r28.m2adec
    0 references
    Q12176
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C26.S1.XMD3.m1dec
    0 references
    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1dec
    0 references
    Q12228
    Defining formula
    A k subscript 𝐴 𝑘 {\displaystyle{\displaystyle A_{k}}}
    xml-id
    C26.S18.XMD1.m1dec
    0 references
    Q12229
    Defining formula
    S 𝑆 {\displaystyle{\displaystyle S}}
    xml-id
    C26.S18.XMD2.m1dec
    0 references
     
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