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Mirrors > Home > ILE Home > Th. List > df-exp | Unicode version |
Description: Define exponentiation to
nonnegative integer powers. For example,
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() This definition is not meant to be used directly; instead, exp0 10507 and expp1 10510 provide the standard recursive definition. The up-arrow notation is used by Donald Knuth for iterated exponentiation (Science 194, 1235-1242, 1976) and is convenient for us since we don't have superscripts.
10-Jun-2005: The definition was extended to include zero exponents, so
that
4-Jun-2014: The definition was extended to include negative integer
exponents. For example, |
Ref | Expression |
---|---|
df-exp |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cexp 10502 |
. 2
![]() ![]() | |
2 | vx |
. . 3
![]() ![]() | |
3 | vy |
. . 3
![]() ![]() | |
4 | cc 7797 |
. . 3
![]() ![]() | |
5 | cz 9239 |
. . 3
![]() ![]() | |
6 | 3 | cv 1352 |
. . . . 5
![]() ![]() |
7 | cc0 7799 |
. . . . 5
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8 | 6, 7 | wceq 1353 |
. . . 4
![]() ![]() ![]() ![]() |
9 | c1 7800 |
. . . 4
![]() ![]() | |
10 | clt 7979 |
. . . . . 6
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11 | 7, 6, 10 | wbr 4000 |
. . . . 5
![]() ![]() ![]() ![]() |
12 | cmul 7804 |
. . . . . . 7
![]() ![]() | |
13 | cn 8905 |
. . . . . . . 8
![]() ![]() | |
14 | 2 | cv 1352 |
. . . . . . . . 9
![]() ![]() |
15 | 14 | csn 3591 |
. . . . . . . 8
![]() ![]() ![]() ![]() |
16 | 13, 15 | cxp 4621 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | 12, 16, 9 | cseq 10428 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
18 | 6, 17 | cfv 5212 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
19 | 6 | cneg 8116 |
. . . . . . 7
![]() ![]() ![]() |
20 | 19, 17 | cfv 5212 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
21 | cdiv 8615 |
. . . . . 6
![]() ![]() | |
22 | 9, 20, 21 | co 5869 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 11, 18, 22 | cif 3534 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 8, 9, 23 | cif 3534 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
25 | 2, 3, 4, 5, 24 | cmpo 5871 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
26 | 1, 25 | wceq 1353 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
This definition is referenced by: exp3val 10505 |
Copyright terms: Public domain | W3C validator |