Which of the following sets is equal to {1, 2, 3, ...}?

{x | x R, x ≥ 1}
{x | x R, x > 1}
{x | x N, x ≥ 1}

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MrRoyal MrRoyal · Answer 1 · 2022-07-29T18:02:03+02:00

From the list of options, the set that is equal to the set {1, 2, 3, ...} is {x | x N, x ≥ 1}

The set is given as:

{1, 2, 3, ...}

The three dots (...) after 3 implies that the elements of the set include other values such as 4, 5, 6 and so on

Using the above scenario, we can see that the set {1, 2, 3, ...} contains only positive integers.

All positive integers are natural numbers and they are denoted by N

From the list of options, we have:

{x | x R, x ≥ 1}

This represents the set of all real numbers greater than or equal to 1.

Note that this set includes decimal numbers i.e. 1, 1.5, 1.89 and so on

This does not represent the set {1, 2, 3, ...}

{x | x R, x > 1}

This represents the set of all real numbers greater than 1.

Note that this set includes decimal numbers i.e. 1.5, 1.89 and so on

This does not represent the set {1, 2, 3, ...}

{x | x N, x ≥ 1}

This represents the set of all natural numbers greater than or equal to 1.

Note that this set does not include decimal numbers i.e. 1, 2, 3, 4 and so on

This does represent the set {1, 2, 3, ...}

Hence, the set that is equal to the set {1, 2, 3, ...} is {x | x N, x ≥ 1}