The natural logarithm is real-valued for all nonnegative real numbers. As it approaches 0 from the right it becomes more and more negative, and at 0 it takes on the value negative infinity. Since in J infinity is denoted by the underbar _ and the negative sign prefixed to a number is also denoted by underbar, negative infinity is denoted by __ , which in most fonts looks like a long underbar.

   ^. 0  NB. ^. is natural logarithm
__

See the division table below for one of the reasons why 0%0 is 0 , particularly by the row headed 0 and the column headed 0 :

   v=._3 _2 _1 0 1 2 3
   (|. by ] over (|.%/]))v
┌──┬──────────────────────────────────────┐
│  │       _3   _2 _1  0  1    2         3│
├──┼──────────────────────────────────────┤
│ 3│       _1 _1.5 _3  _  3  1.5         1│
│ 2│_0.666667   _1 _2  _  2    1  0.666667│
│ 1│_0.333333 _0.5 _1  _  1  0.5  0.333333│
│ 0│        0    0  0  0  0    0         0│
│_1│ 0.333333  0.5  1 __ _1 _0.5 _0.333333│
│_2│ 0.666667    1  2 __ _2   _1 _0.666667│
│_3│        1  1.5  3 __ _3 _1.5        _1│
└──┴──────────────────────────────────────┘

The utility verbs by and over are defined on Lay it on the table.