Deleted Neighborhood
The proper name for a set such as {x:
0 < x – a < δ}.
Deleted neighborhoods are encountered in the study of limits.
It is the set of all numbers less than δ units
away from a, omitting the number a itself.
Using interval
notation the set {x: 0 < x – a < δ} would
be (a – δ, a) ∪ (a,
a + δ). In general, a deleted neighborhood of a is
any set (c, a) ∪ (a, d) where c < a < d.
For example, one deleted neighborhood of 2 is the set {x:
0 < x – 2 < 0.1}, which is the same as (1.9,
2) ∪ (2,
2.1).
See
also
Neighborhood, setbuilder
notation, interval notation
