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Let $A = {2x : x ∈ Z, -16 <= x <= 4}$.

What is the cardinality of this set?

What would be the translation of this to plain english?

as4s4hetic
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calimses
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  • Translation into english? How many elements does the following set have, if the set is infinite are the elements countable, in one to one correspondence with the reals, or some other size? the set is the set of all even numbers from 2x(-16) to 2x4. Be sure to include 2x (-16) and 2x4 in your set. – fleablood May 09 '17 at 05:59

2 Answers2

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Cardinality is in layman's term the size of the set. For the set $A = \left\{ 2x : x \in \mathbb{Z} , -16 \leq x \leq 4 \right\}$ we can simply list out all the elements explicitly, we have that $$A = \left\{ -32 , -30, -28, -26, -24, -22, -20, -18, -16, -14, -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8 \right\}$$ Counting the number of elements we find out that the cardinality of the set is $21$.

Dragonite
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The cardinality is the amount of elements in a given set.

For your set, $A = \left\{2x:x\in \mathbb{Z},-16\leq x\leq4\right\}$, $x$ takes on integer values between $-16$ and $4$.

Note $2x$ is the condition that defines each element of the set, given some $x$ in the bounded interval $[-16,4]$. Therefore, for each input $x$, you get a corresponding mapping/output $2x$.

So, the cardinality is simply the amount of countable integers in the bounded interval $[-16,4]$

We note $x$ can take on values of: $-16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4$

So, the cardinality is $21$.

Note, to obtain the actual set, simply multiply each $x$ input by $2$.

Mark Pineau
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