Set Definition by Predicate/Examples/Set Indexed by Natural Numbers between 1 and 100

Examples of Set Definition by Predicate

Let $V$ be the set defined as:

$V := \set {v_i: 1 \le i \le 100, i \in \N}$

Then $V$ is the set of the $100$ elements:

$V = \set {v_1, v_2, \ldots, v_{100} }$

and can also be written:

$V := \set {v_i: i = 1, 2, \ldots, 100}$

or even:

$V := \set {v_i: 1 \le i \le 100}$

as it is understood that the domain of $i$ is the set of natural numbers.

Sources

• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Appendix $\text{A}.1$: Sets and Subsets