3) The art of thinking about your thinking while you are thinking in order to make your thinking better: more clear, more accurate, or more defensible. Critical thinking can be distinguished into two forms: "selfish" or "sophistic", on the one hand, and "fairminded", on the other. In thinking critically we use our command of the elements of thinking to adjust our thinking successfully to the logical demands of a type or mode of thinking. See critical person, critical society, critical reading, critical listening, critical writing, perfections of thought, elements of thought, domains of thought, intellectual virtues.

At the end of 2 nd week the state vector is
Px 1

x (2) =
Px (1)
=
|.25
.20
.25
.30|
|.25|
=
|.2550 |
|.20
.30
.25
.30|
|.20|
=
|.2625 |
|.25
.20
.40
.10|
|.25|
=
|.2325 |
|.30
.30
.10
.30|
|.30|
=
|.2500 |

Note that we can compute x 2 directly using
x 0 as
x (2) = Px (1) = P(Px (0) ) =
P 2 x (0)
Similarly, we can find the state vector for 5 th , 10 th , 20 th , 30 th , and 50 th observation periods.
x (5) =
P 5 x (0) =
.2495
.2634
.2339
.2532
x (10) =
P 10 x (0) =
.2495
.2634
.2339
.2532
x (20) =
P 20 x (0) =
.2495
.2634
.2339
.2532
x (30) =
.2495
.2634
.2339
.2532

x (50) =
.2495
.2634
.2339
.2532

The same limiting results can be obtained by solving the linear system of equations P P = P using this JavaScript. It suggests that the state vector approached some fixed vector, as the number of observation periods increase. This is not the case for every Markov Chain. For example, if
P =
0
1
1
0
, and