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Floor <.  0 0 0 Lesser Of (Min)

<.y gives the floor of y , that is, the largest integer less than or equal to y . Thus:
   <. 4.6 4 _4 _4.6
4 4 _4 _5
The implied comparison with integers is tolerant, as discussed under Equal (=), and is controlled by <.!.t . See below for complex arguments.
 		   x<.y is the lesser of x and y . For example:
   3 <. 4 _4
3 _4

   <./7 8 5 9 2
2

   <./\7 8 5 9 2
7 7 5 5 2

For a complex argument, the definition of <. is modelled by:
   floor=: j./@(ip+(c2>c1),c1+:c2)
   '`c1 c2 fp ip'=:(1:>+/@fp)`(>:/@fp)`(+.-ip)`(<.@+.)
As developed by McDonnell [10], this function has the following properties:

Convexity: If (<.z1)=(<.z2) and z3 lies on the line between z1 to z2, then (<.z3)=(<.z1) .
Translatability:  If z4 is a Gaussian integer, then (z4+<.z5)=(<.z4+z5) .
Compatibility: (<.x j.0)=((<.x)j.0) and (<.0 j.x)=(0 j.(<.x))

The function <. can be viewed as a tiling by rectangles of unit area, all arguments within a rectangle sharing the same floor. One rectangle has vertices at 1j0 and 0j1, with the other side passing through the origin. Rectangles along successive diagonals are displaced by one-half the length.

The phrase j./@ip “floors” the individual parts of a complex argument. Moreover, the floor <.y is equivalent to ->.-y . In other words, it is the dual of ceiling with respect to (that is, under) arithmetic negation: <. ↔ >.&.- and >. ↔ <.&.- . Thus:
   (>.&.- ; <.) 4.6 4 _4 _4.6
+---------+---------+
|4 4 _4 _5|4 4 _4 _5|
+---------+---------+
The expression <.x+0.5 gives the integer nearest to the real argument x . The number of digits needed to represent a positive integer is given by one plus the floor of its base ten logarithm:
   a ,. (,. 1:+<.) 10^. a=: 9 10 11 99 100 101
  9 0.954243 1
 10        1 2
 11  1.04139 2
 99  1.99564 2
100        2 3
101  2.00432 3

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