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Mirrors > Home > ILE Home > Th. List > df-bc | Unicode version |
Description: Define the binomial
coefficient operation. For example,
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]()
In the literature, this function is often written as a column vector of
the two arguments, or with the arguments as subscripts before and after
the letter "C". |
Ref | Expression |
---|---|
df-bc |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbc 10525 |
. 2
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2 | vn |
. . 3
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3 | vk |
. . 3
![]() ![]() | |
4 | cn0 9001 |
. . 3
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5 | cz 9078 |
. . 3
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6 | 3 | cv 1331 |
. . . . 5
![]() ![]() |
7 | cc0 7644 |
. . . . . 6
![]() ![]() | |
8 | 2 | cv 1331 |
. . . . . 6
![]() ![]() |
9 | cfz 9821 |
. . . . . 6
![]() ![]() | |
10 | 7, 8, 9 | co 5782 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() |
11 | 6, 10 | wcel 1481 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
12 | cfa 10503 |
. . . . . 6
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13 | 8, 12 | cfv 5131 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() |
14 | cmin 7957 |
. . . . . . . 8
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15 | 8, 6, 14 | co 5782 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() |
16 | 15, 12 | cfv 5131 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | 6, 12 | cfv 5131 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() |
18 | cmul 7649 |
. . . . . 6
![]() ![]() | |
19 | 16, 17, 18 | co 5782 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | cdiv 8456 |
. . . . 5
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21 | 13, 19, 20 | co 5782 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
22 | 11, 21, 7 | cif 3479 |
. . 3
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23 | 2, 3, 4, 5, 22 | cmpo 5784 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 1, 23 | wceq 1332 |
1
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Colors of variables: wff set class |
This definition is referenced by: bcval 10527 |
Copyright terms: Public domain | W3C validator |