Cauchy distribution limits

I have question (curiosity) regarding returned values of R's qcauchy 
() function,
for nonexceedance probability (F). It seems the ideal returned range  
of cauchy distribution should be [-Inf,Inf].

For F=0
 > qcauchy(0)
[1] -Inf

but for F=1
 > qcauchy(1)
[1] 8.16562e+15

It seems to me that the proper return value should be Inf???

For default (location=0,scale=1) quantile function of cauchy

x(F) = tan(pi * (F - 0.5))

For F = 0
 > tan(pi*(-0.5))
[1] -1.633124e+16

For F = 1
 > tan(pi*(0.5))
[1] 1.633124e+16

So I conclude that qcauchy(0) properly handles the -Inf result and  
the qcauchy(1) returns a very large number, curiously not equal to tan 
(0.5*pi), but certainly not Inf.

As double check,
 > tan(pi*(0.99999-0.5))
[1] 31830.99
 > qcauchy(0.99999)
[1] 31830.99

william