Is it necessary to write about the set?

Question

I have this set, represented by extension:

$\{1, 2, 4, 8, 16, 32, 64, 128, ...\}$

Now I must represent it by comprehension:

$$\{x \in \mathbb{N} : 2^{x-1} \text{ is power of } 2\}$$

Is it necessary to write "is power of 2" ?

Answer 1

The set you must represent has the following form:

$$ \{2^n: \, 0 \le n \le 7\} $$

Answer 2

$$A=\{1, 2, 4, 8, 16, 32, 64, ...\}$$ $$A=\{2^{n-1}|n\in \mathbb {N} \}$$

$$A=\{x| x=2^{n-1},n\in \mathbb {N} \}$$

Answer 3

$\{1, 2, 4, 8, 16, 32, 64, 128... +\infty\}$
= { $2^n$ : n non-negative integer }
= { n : n = $2^k$ for some non-negative integer k }.

Answer 4

Another way would be

$$\{ x \in \mathbb{N} \; | \; \exists n \in \mathbb{N}, \; x = 2^{n-1} \},$$

which would be read aloud as "the set of all $x$ in $\mathbb{N}$ such that there exists an $n$ in $\mathbb{N}$ where $x = 2^{n-1}$."