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|00000000| 5c 73 65 63 74 69 6f 6e | 7b 65 70 73 69 6c 6f 6e |\section|{epsilon|
|00000010| 20 2d 2d 2d 20 43 6f 6d | 70 75 74 65 20 6d 61 63 | --- Com|pute mac|
|00000020| 68 69 6e 65 20 65 70 73 | 69 6c 6f 6e 7d 0d 5c 6c |hine eps|ilon}.\l|
|00000030| 61 62 65 6c 7b 66 6e 3a | 65 70 73 69 6c 6f 6e 7d |abel{fn:|epsilon}|
|00000040| 0d 5c 69 6e 64 65 78 7b | 65 70 73 69 6c 6f 6e 28 |.\index{|epsilon(|
|00000050| 29 7d 0d 5c 69 6e 64 65 | 78 7b 6d 61 63 68 69 6e |)}.\inde|x{machin|
|00000060| 65 20 65 70 73 69 6c 6f | 6e 7d 0d 5c 62 65 67 69 |e epsilo|n}.\begi|
|00000070| 6e 7b 72 61 69 6c 7d 0d | 45 70 73 69 6c 6f 6e 20 |n{rail}.|Epsilon |
|00000080| 3a 20 27 65 70 73 69 6c | 6f 6e 27 20 27 28 27 20 |: 'epsil|on' '(' |
|00000090| 27 29 27 20 3b 0d 5c 65 | 6e 64 7b 72 61 69 6c 7d |')' ;.\e|nd{rail}|
|000000a0| 0d 0d 5c 76 65 72 62 2b | 65 70 73 69 6c 6f 6e 2b |..\verb+|epsilon+|
|000000b0| 20 63 61 6c 63 75 6c 61 | 74 65 73 20 74 68 65 20 | calcula|tes the |
|000000c0| 65 70 73 69 6c 6f 6e 20 | 6f 66 20 74 68 69 73 20 |epsilon |of this |
|000000d0| 6d 61 63 68 69 6e 65 2e | 20 20 45 70 73 69 6c 6f |machine.| Epsilo|
|000000e0| 6e 0d 69 73 20 64 65 66 | 69 6e 65 64 20 61 73 20 |n.is def|ined as |
|000000f0| 74 68 65 20 6c 61 72 67 | 65 73 74 20 6e 75 6d 62 |the larg|est numb|
|00000100| 65 72 20 79 6f 75 20 63 | 61 6e 20 61 64 64 20 74 |er you c|an add t|
|00000110| 6f 20 24 31 24 20 61 6e | 64 20 67 65 74 20 61 0d |o $1$ an|d get a.|
|00000120| 72 65 73 75 6c 74 20 74 | 68 61 74 20 69 73 20 69 |result t|hat is i|
|00000130| 6e 64 69 73 63 65 72 6e | 61 62 6c 65 20 66 72 6f |ndiscern|able fro|
|00000140| 6d 20 24 31 24 2e 20 20 | 54 68 65 72 65 20 69 73 |m $1$. |There is|
|00000150| 20 61 20 76 61 72 69 61 | 62 6c 65 2c 0d 5c 76 65 | a varia|ble,.\ve|
|00000160| 72 62 2b 65 70 73 2b 2c | 20 74 68 61 74 20 69 73 |rb+eps+,| that is|
|00000170| 20 61 75 74 6f 6d 61 74 | 69 63 61 6c 6c 79 20 70 | automat|ically p|
|00000180| 6c 61 63 65 64 20 69 6e | 74 6f 20 74 68 65 20 67 |laced in|to the g|
|00000190| 6c 6f 62 61 6c 20 73 79 | 6d 62 6f 6c 20 74 61 62 |lobal sy|mbol tab|
|000001a0| 6c 65 0d 62 79 20 74 68 | 65 20 64 65 66 61 75 6c |le.by th|e defaul|
|000001b0| 74 20 5c 76 65 72 62 2b | 2e 72 6c 61 62 2b 20 66 |t \verb+|.rlab+ f|
|000001c0| 69 6c 65 2e 20 20 59 6f | 75 20 6d 61 79 20 66 69 |ile. Yo|u may fi|
|000001d0| 6e 64 20 74 68 65 20 76 | 61 72 69 61 62 6c 65 20 |nd the v|ariable |
|000001e0| 6d 6f 72 65 0d 63 6f 6e | 76 65 6e 69 65 6e 74 20 |more.con|venient |
|000001f0| 74 6f 20 75 73 65 20 74 | 68 61 6e 20 74 68 65 20 |to use t|han the |
|00000200| 66 75 6e 63 74 69 6f 6e | 2c 20 61 6e 64 20 74 68 |function|, and th|
|00000210| 65 20 65 78 70 65 6e 73 | 65 20 6f 66 20 70 6f 73 |e expens|e of pos|
|00000220| 73 69 62 6c 65 0d 70 6f | 72 74 61 62 6c 69 74 79 |sible.po|rtablity|
|00000230| 20 70 72 6f 62 6c 65 6d | 73 2e 0d 0d 24 5c 4c 6f | problem|s...$\Lo|
|00000240| 6e 67 72 69 67 68 74 61 | 72 72 6f 77 24 20 54 68 |ngrighta|rrow$ Th|
|00000250| 69 73 20 69 73 20 6e 6f | 74 20 61 6e 20 5c 52 4c |is is no|t an \RL|
|00000260| 61 42 5c 20 62 75 69 6c | 74 2d 69 6e 20 66 75 6e |aB\ buil|t-in fun|
|00000270| 63 74 69 6f 6e 2e 20 20 | 54 68 69 73 20 66 75 6e |ction. |This fun|
|00000280| 63 74 69 6f 6e 0d 69 73 | 20 6e 6f 72 6d 61 6c 6c |ction.is| normall|
|00000290| 79 20 6c 6f 61 64 65 64 | 20 6f 6e 20 73 74 61 72 |y loaded| on star|
|000002a0| 74 2d 75 70 20 66 72 6f | 6d 20 74 68 65 20 5c 76 |t-up fro|m the \v|
|000002b0| 65 72 62 2b 65 70 73 69 | 6c 6f 6e 2e 72 2b 20 66 |erb+epsi|lon.r+ f|
|000002c0| 69 6c 65 20 69 6e 20 74 | 68 65 0d 73 74 61 6e 64 |ile in t|he.stand|
|000002d0| 61 72 64 20 5c 76 65 72 | 62 2b 72 6c 69 62 2b 20 |ard \ver|b+rlib+ |
|000002e0| 64 69 72 65 63 74 6f 72 | 79 2e 20 55 73 65 20 6f |director|y. Use o|
|000002f0| 66 20 74 68 65 20 5c 76 | 65 72 62 2b 2d 72 2b 20 |f the \v|erb+-r+ |
|00000300| 6f 70 74 69 6f 6e 2c 20 | 69 6e 63 6f 72 72 65 63 |option, |incorrec|
|00000310| 74 6c 79 20 0d 73 65 74 | 74 69 6e 67 20 74 68 65 |tly .set|ting the|
|00000320| 20 5c 76 65 72 62 2b 52 | 4c 41 42 5f 4c 49 42 5f | \verb+R|LAB_LIB_|
|00000330| 44 49 52 2b 20 65 6e 76 | 69 72 6f 6e 6d 65 6e 74 |DIR+ env|ironment|
|00000340| 61 6c 20 76 61 72 69 61 | 62 6c 65 2c 20 6f 72 20 |al varia|ble, or |
|00000350| 6d 6f 64 69 66 79 69 6e | 67 0d 5c 76 65 72 62 2b |modifyin|g.\verb+|
|00000360| 65 70 73 69 6c 6f 6e 2e | 72 2b 20 6d 61 79 20 6d |epsilon.|r+ may m|
|00000370| 61 6b 65 20 74 68 69 73 | 20 66 75 6e 63 74 69 6f |ake this| functio|
|00000380| 6e 20 75 6e 61 76 61 69 | 6c 61 62 6c 65 2e 0d 0d |n unavai|lable...|
|00000390| 0d 5c 70 61 72 61 67 72 | 61 70 68 7b 45 78 61 6d |.\paragr|aph{Exam|
|000003a0| 70 6c 65 7d 0d 5c 69 6e | 64 65 78 7b 65 78 61 6d |ple}.\in|dex{exam|
|000003b0| 70 6c 65 20 6f 66 20 65 | 70 73 69 6c 6f 6e 28 29 |ple of e|psilon()|
|000003c0| 7d 0d 5c 69 6e 64 65 78 | 7b 65 70 73 69 6c 6f 6e |}.\index|{epsilon|
|000003d0| 28 29 21 65 78 61 6d 70 | 6c 65 7d 0d 5c 62 65 67 |()!examp|le}.\beg|
|000003e0| 69 6e 7b 76 65 72 62 61 | 74 69 6d 7d 0d 3e 20 65 |in{verba|tim}.> e|
|000003f0| 70 73 69 6c 6f 6e 28 29 | 0d 20 31 2e 31 31 65 2d |psilon()|. 1.11e-|
|00000400| 31 36 0d 3e 20 65 70 73 | 0d 20 65 70 73 20 3d 0d |16.> eps|. eps =.|
|00000410| 20 31 2e 31 31 65 2d 31 | 36 0d 3e 20 31 2b 65 70 | 1.11e-1|6.> 1+ep|
|00000420| 73 69 6c 6f 6e 28 29 3d | 3d 31 0d 20 20 20 20 20 |silon()=|=1. |
|00000430| 20 20 20 31 0d 3e 20 31 | 2b 32 2a 65 70 73 69 6c | 1.> 1|+2*epsil|
|00000440| 6f 6e 28 29 3d 3d 31 0d | 20 20 20 20 20 20 20 20 |on()==1.| |
|00000450| 30 0d 5c 65 6e 64 7b 76 | 65 72 62 61 74 69 6d 7d |0.\end{v|erbatim}|
|00000460| 0d 0d 5c 6e 65 77 70 61 | 67 65 0d 0d 0d 0d |..\newpa|ge.... |
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