a < b < c is alway TRUE

In R like C, FALSE is 0 and TRUE is 1.  This is a bad thing, but it's
too late to change it now.  With that substitution, all the results
look reasonable:  0>1, 1<1 and 1>1 are all false, but 0<1 is true.

Why a bad thing?  Because it leads to absurdities like this whole
thread has been discussing!

What should they have done?  They should have done what Fortran,
Pascal, etc. do, and have a separate logical or boolean type that
isn't automatically converted to a numerical type.  In Pascal for
instance, "3 < 2 < 1" is flagged as a syntax error, because you can't
compare a boolean to an integer.  If you really want to do the weird
comparison that R is doing, you need to enter it as "ord(3 < 2) < 1",
and any reader will see that you're doing something weird.

Well, actually R does have a separate logical type for precisely this
reason. That's why, say
  2+2==4
evaluates to TRUE in R, not to 1, and why logical subscripts are different
from integer subscripts
For example
  x[is.na(x)]
returns the non-missing elements of x, but x[as.numeric(is.na(x))] returns
as many copies of the first elements as there are missing elements.

The feature/bug/wart in R that causes this whole discussion is that
numerical operators in R try to coerce their arguments to numbers, so that
if a or b is logical in
  a<b
we actually evaluate
  as.numeric(a)<as.numeric(b)

Also, we coerce going the other way in if() statements, to make
	if(length(x))
work. This latter coercion is relatively recent and was done for
compatibility with C programmers writing in S.

Certainly a<b<c has no sensible use: if c is numeric it is nonense and if
c is logical it is c & !(a<b).  I would even contend that it is a bad sign
if you know what
	3<2<1
will evaluate to without careful thought or testing on a copy of R.


	-thomas

Thomas Lumley			Asst. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle

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