# What is the cardinality of this set

## Mightiness

In this chapter we look at what is meant by the power of a crowd.

Basic knowledge of set theory is assumed to be known.

The power of a crowd means that **Number of elements** this crowd.

Notation: \ (| A | \)

**example**

The amount

\ (A = \ {\ text {dog, cat, mouse} \} \)

has three elements.

The cardinality of the set \ (A \) is 3.

The following applies: \ (| A | = 3 \).

### Determine the thickness of a crowd

According to the motto "Practice makes perfect!" let's look at some more examples:

\ (A = \ {1,3,5,7,9 \} \ qquad \ Rightarrow \ quad | A | = 5 \)

\ (B = \ {x, y, z \} \ qquad \ Rightarrow \ quad | B | = 3 \)

\ (C = \ {\ text {Munich, Hamburg, Berlin, Cologne} \} \ qquad \ Rightarrow \ quad | C | = 4 \)

So when the power of a crowd is asked, it's about the **Number of elements** to determine. In most cases, you simply have to count the elements.

### More about set theory

In connection with set theory, there are some topics that are repeatedly asked about in exams. It is therefore worthwhile to work through the following chapters one after the other.

*Note:*To define mathematical symbols, a colon is usually used in front of an equal sign, with the expression on the left (next to the colon) being defined by the other. The colon equals sign \ (: = \) is spoken "

*is by definition the same*Often the colon is simply left out.

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