Activation Descriptions
Qwen/Qwen3-8B · layer 18/36 · 242 tokens · /home/slava/projects/cco_checkpoints/grpo_Qwen3-8B_n40k_final
Let
f
(x
)
be
defined
for
all
x
≠
a
over
an
open
interval
containing
a
.
Let
L
be
a
real
number
.
Then
the
limit
of
f
(x
)
as
x
approaches
a
is
L
,
written
lim
_{
x
→
a
}
f
(x
)
=
L
,
if
for
every
ε
>
0
,
there
exists
a
δ
>
0
such
that
if
0
<
|
x
−
a
|
<
δ
,
then
|
f
(x
)
−
L
|
<
ε
.
This
definition
is
known
as
the
epsilon
-d
elta
definition
of
a
limit
.
Int
uit
ively
,
this
means
that
for
any
desired
degree
of
clos
eness
ε
to
L
,
we
can
find
a
small
enough
interval
around
a
such
that
all
values
of
f
(x
)
for
x
in
that
interval
(
except
possibly
x
=
a
itself
)
are
within
ε
of
L
.
The
definition
does
not
require
f
to
be
defined
at
x
=
a
,
nor
does
it
require
f
(a
)
=
L
when
f
is
defined
there
.
The
epsilon
-d
elta
formulation
,
first
developed
rigor
ously
by
Karl
We
ier
str
ass
in
the
1
8
7
0
s
,
placed
calculus
on
a
firm
logical
foundation
after
nearly
two
centuries
of
informal
use
of
limits
by
Newton
,
Le
ib
n
iz
,
and
their
successors
.
Click a token above to see its activation description.
Click tokens or use arrow keys to navigate.