To simplify the expression
[
(1 - \frac{1}{2})(1 - \frac{1}{3})(1 - \frac{1}{4}) \cdots (1 - \frac{1}{2023}),
]
we will first simplify each individual term:
[
1 - \frac{1}{n} = \frac{n-1}{n}.
]
So the product becomes:
[
\frac{1}{2} \cdot \frac{2}{3} \cdot \frac{3}{4} \cdots \frac{2022}{2023}.
]
Now let's write this out as a single fraction:
[
\frac{1}{2} \cdot \frac{2}{3} \cdot \frac{3}{4} \cdots \frac{2022}{2023} = \frac{1 \cdot 2 \cdot 3 \cdots \cdot 2022}{2 \cdot 3 \cdot 4 \cdots \cdot 2023}.
]
Notice that the numerator ( 1 \cdot 2 \cdot 3 \cdots \cdot 2022 ) is ( 2022! ), and the denominator is:
[
2 \cdot 3 \cdot 4 \cdots \cdot 2023 = \frac{2023!}{1},
]
because ( 2023! = 1 \cdot 2 \cdot 3 \cdots \cdot 2023 ).
Thus, we can rewrite the entire product as:
[
\frac{2022!}{2023!} = \frac{2022!}{2023 \cdot 2022!} = \frac{1}{2023}.
]
Finally, the value of the original product
[
(1 - \frac{1}{2})(1 - \frac{1}{3})(1 - \frac{1}{4}) \cdots (1 - \frac{1}{2023})
]
is
[
\frac{1}{2023}.
]
Hence, the final result is
[
\boxed{\frac{1}{2023}}.
]
