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LaTeX Document  |  1992-11-04  |  7.4 KB

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This file was processed as: LaTeX Document (document/latex).

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100% dexvert Newsgroup Content (archive/news) magic Supported
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99% file LaTeX document, ASCII text default
100% checkBytes Printable ASCII default
100% dexmagic PrintFox/Pagefox WEAK default
100% perlTextCheck Likely Text (Perl) default
100% detectItEasy Format: plain text[LF] default (weak)
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|00001a60| 24 2c 20 6f 72 20 24 5c | 72 61 6e 6b 0a 28 78 29 |$, or $\|rank.(x)|
|00001a70| 24 2c 20 6f 66 20 61 20 | 77 65 6c 6c 2d 66 6f 75 |$, of a |well-fou|
|00001a80| 6e 64 65 64 20 73 65 74 | 20 24 78 24 20 69 73 20 |nded set| $x$ is |
|00001a90| 74 68 65 20 6c 65 61 73 | 74 20 6f 72 64 69 6e 61 |the leas|t ordina|
|00001aa0| 6c 20 24 5c 62 65 74 61 | 24 20 73 75 63 68 20 74 |l $\beta|$ such t|
|00001ab0| 68 61 74 20 24 78 0a 5c | 73 75 62 73 65 74 65 71 |hat $x.\|subseteq|
|00001ac0| 20 52 28 5c 62 65 74 61 | 29 24 3a 20 24 24 5c 72 | R(\beta|)$: $$\r|
|00001ad0| 68 6f 20 28 78 29 20 5c | 44 66 20 28 5c 6d 75 20 |ho (x) \|Df (\mu |
|00001ae0| 5c 62 65 74 61 29 20 5c | 73 71 64 6f 74 20 5c 4f |\beta) \|sqdot \O|
|00001af0| 72 64 20 28 5c 62 65 74 | 61 29 20 5c 73 71 64 6f |rd (\bet|a) \sqdo|
|00001b00| 74 20 78 0a 5c 73 75 62 | 73 65 74 65 71 20 52 28 |t x.\sub|seteq R(|
|00001b10| 5c 62 65 74 61 29 2e 24 | 24 0a 5c 65 6e 64 7b 64 |\beta).$|$.\end{d|
|00001b20| 65 66 6e 7d 0a 0a 28 59 | 6f 75 20 6d 61 79 20 68 |efn}..(Y|ou may h|
|00001b30| 61 76 65 20 74 6f 20 6d | 61 6b 65 20 73 6f 6d 65 |ave to m|ake some|
|00001b40| 20 6f 62 76 69 6f 75 73 | 20 61 64 6a 75 73 74 6d | obvious| adjustm|
|00001b50| 65 6e 74 73 20 74 6f 20 | 63 6f 6d 70 69 6c 65 20 |ents to |compile |
|00001b60| 74 68 69 73 2e 29 0a 0a | 42 65 69 6e 67 20 74 68 |this.)..|Being th|
|00001b70| 61 74 20 61 6e 20 65 71 | 75 69 76 61 6c 65 6e 74 |at an eq|uivalent|
|00001b80| 20 66 6f 72 6d 20 6f 66 | 20 74 68 65 20 41 78 69 | form of| the Axi|
|00001b90| 6f 6d 20 6f 66 20 46 6f | 75 6e 64 61 74 69 6f 6e |om of Fo|undation|
|00001ba0| 20 69 73 20 74 68 61 74 | 20 61 6c 6c 0a 73 65 74 | is that| all.set|
|00001bb0| 73 20 61 72 65 20 77 65 | 6c 6c 2d 66 6f 75 6e 64 |s are we|ll-found|
|00001bc0| 65 64 2c 20 75 6e 64 65 | 72 20 74 68 65 73 65 20 |ed, unde|r these |
|00001bd0| 64 65 66 69 6e 69 74 69 | 6f 6e 73 20 65 61 63 68 |definiti|ons each|
|00001be0| 20 73 65 74 20 68 61 73 | 20 61 20 72 61 6e 6b 2e | set has| a rank.|
|00001bf0| 0a 0a 3e 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |..>-----|--------|
|00001c00| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001c10| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001c20| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001c30| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001c40| 2d 0a 3e 20 20 20 20 20 | 20 20 20 20 20 20 20 42 |-.> | B|
|00001c50| 69 6c 6c 20 54 61 79 6c | 6f 72 20 20 20 20 20 20 |ill Tayl|or |
|00001c60| 20 20 20 20 20 20 20 20 | 77 66 74 40 6d 61 74 68 | |wft@math|
|00001c70| 2e 63 61 6e 74 65 72 62 | 75 72 79 2e 61 63 2e 6e |.canterb|ury.ac.n|
|00001c80| 7a 0a 3e 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |z.>-----|--------|
|00001c90| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001ca0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001cb0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001cc0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001cd0| 2d 0a 3e 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |-.> | |
|00001ce0| 20 20 20 20 20 20 49 20 | 74 68 69 6e 6b 2c 20 74 | I |think, t|
|00001cf0| 68 65 72 65 66 6f 72 65 | 20 49 20 61 6d 3b 20 28 |herefore| I am; (|
|00001d00| 49 20 74 68 69 6e 6b 29 | 2e 0a 3e 2d 2d 2d 2d 2d |I think)|..>-----|
|00001d10| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001d20| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001d30| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001d40| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001d50| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 0a 0a 63 6f 72 64 69 |--------|-..cordi|
|00001d60| 61 6c 6c 79 2c 0a 6d 69 | 6b 68 61 69 6c 20 7a 65 |ally,.mi|khail ze|
|00001d70| 6c 65 6e 79 40 68 75 73 | 63 2e 68 61 72 76 61 72 |leny@hus|c.harvar|
|00001d80| 64 2e 65 64 75 0a 22 20 | 2d 2d 20 49 20 73 68 61 |d.edu." |-- I sha|
|00001d90| 6c 6c 20 73 70 65 61 6b | 20 62 6c 75 6e 74 6c 79 |ll speak| bluntly|
|00001da0| 2c 20 62 65 63 61 75 73 | 65 20 6c 69 66 65 20 69 |, becaus|e life i|
|00001db0| 73 20 73 68 6f 72 74 2e | 22 0a |s short.|". |
+--------+-------------------------+-------------------------+--------+--------+