Question

What are two other ways to name Z

Answer 1

The given set ℤ can be written as {..., -3, -2, -1, 0, 1, 2, 3, ...}.

The given set ℤ can be written as { x | x is an integer, -∞ < x < ∞}.

Disclaimer:

I assume that ℤ in the question indicates the set of all integers.

Sets are the basis of mathematics. One can write sets in different ways and form smaller sets of elements from a larger set.

Any set can be written in two forms.

1. Roster form
2. Set-builder notation

Roster form:

Roster form is one way to write sets. The roster form lists the elements of a set within braces, { }. Let's see a few examples for the roster form.

1. We write the set containing the elements 5, 6, 7, and 8 as {5, 6, 7, 8}
2. We write the set of multiples of 5 as {5, 10, 15, 20, 25, 30,...}.

So, the given set ℤ can be written as {..., -3, -2, -1, 0, 1, 2, 3, ...}

Set-builder notation:

Set-builder notation is another way to write sets. Set-builder notation describes by enumerating its elements or stating the properties that its elements must satisfy. Let's see a few examples for the set-builder notation.

1. We write the set containing the elements 5, 6, 7, and 8 as { x | x is a natural number, 4 < x < 9}
2. We can write the set of multiples of 5 as { x | x is a multiple of 5}. This is read as "the set of all real numbers x, such that x is a multiple of 5".

So, the given set ℤ can be written as { x | x is an integer, -∞ < x < ∞}. This is read as "the set of all real numbers x, such that x is an integer".

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