Element Math Example 4

Follow the full solution, then compare it with the other examples linked below.

medium

Let

T = \{x \in \mathbb{Z} : x^2 < 10\}

. List all elements of

T

and state

|T|

1
Find all integers $x$ with $x^2 < 10$ . Try: $0^2=0$ , $(\pm 1)^2=1$ , $(\pm 2)^2=4$ , $(\pm 3)^2=9$ , $(\pm 4)^2=16 \ge 10$ .
2
So the elements are $-3, -2, -1, 0, 1, 2, 3$ .
3
Count: $|T| = 7$ .

Answer

T = \{-3,-2,-1,0,1,2,3\},\quad |T| = 7

Set-builder notation defines membership by a condition. Test each candidate integer against

x^2 < 10

to determine which belong to

T

About Element

An individual object that belongs to, or is a member of, a given set — either it is in the set or it is not.

Let [formula]. Determine whether [formula], [formula], and [formula].

Let [formula]. Which of the following are true? (a) [formula], (b) [formula], (c) [formula], (d) [fo

Let [formula]. Fill in each blank with [formula] or [formula]: (a) [formula], (b) [formula], (c) [fo