Sinks

Sinks are limit points in a numeric series. That means that discrete values get arbitrarily close to the sink (from the left or right), and there are infinitely many discrete values around the sink. This function returns a matrix of all sinks in the numeric series.

Usage

sinks(x)

Arguments

x

Numeric series (numeric vector or object of class "discretes").

Value

A matrix with two columns: location and direction. Each row corresponds to a sink, where location is the location of the sink (possibly infinite), and direction indicates whether the sink is approached from the left (-1) or right (1).

See also

has_sink_in(), has_sink_at()

Examples

# The set of integers have sinks at +Inf and -Inf
sinks(integers())
#>      location direction
#> [1,]      Inf        -1
#> [2,]     -Inf         1

# The set 1, 1/2, 1/4, 1/8, ... has a sink at 0 approached from the right.
halves <- 0.5^natural0()
sinks(halves)
#>      location direction
#> [1,]        0         1

# The reciprocal of the integers has a sink at 0 approached from both the
# left and right; while the integer 0 gets mapped to Inf, infinity is not a
# sink because discrete values don't get arbitrarily close to it.
reciprocals <- 1 / integers()
sinks(reciprocals)
#>      location direction
#> [1,]        0         1
#> [2,]        0        -1
has_discretes(reciprocals, Inf) # Yet Inf is a discrete value.
#> [1] TRUE