Almost: In set theory, when dealing with sets of infinite size, the term almost or nearly is used to refer to all but a finite amount of negligible elements in the set.More specifically, given an set
S
{\displaystyle S}
that is a subset of another countably infinite set
L
{\displaystyle L}
,
S
{\displaystyle S}
is said to be almost
L
{\displaystyle L}
if the set difference
L
∖
S
{\displaystyle L\backslash S}
is finite in size. Alternatively, if
L
{\displaystyle L}
is uncountable set, then
S
{\displaystyle S}
can also be said to be almost
L
{\displaystyle L}
if
L
∖
S
{\displaystyle L\backslash S}
is countable in size.For example:
The set
S
=
{
n
∈
N

n
≥
k
}
{\displaystyle S=\{n\in \mathbb {N} \,\,n\geq k\}}
is almost
N
{\displaystyle \mathbb {N} }
for any
k
{\displaystyle k}
in
N
{\displaystyle \mathbb {N} }
, because only finitely many natural numbers are less than
k
{\displaystyle k}
.