```

////

## Number validations: floats, greater than and less than

Number validations also work for `float` values.

Here's where it becomes important to be able to declare <abbr title="greater than"><code>gt</code></abbr> and not just <abbr title="greater than or equal"><code>ge</code></abbr>. As with it you can require, for example, that a value must be greater than `0`, even if it is less than `1`.

Validações numéricas também funcionam para valores do tipo `float`.

Aqui é onde se torna importante a possibilidade de declarar <abbr title="greater than"><code>gt</code></abbr> e não apenas <abbr title="greater than or equal"><code>ge</code></abbr>. Com isso você pode especificar, por exemplo, que um valor deve ser maior que `0`, ainda que seja menor que `1`.

La même chose s'applique pour :

* `gt` : `g`reater `t`han
* `le` : `l`ess than or `e`qual

{* ../../docs_src/path_params_numeric_validations/tutorial005_an_py39.py hl[10] *}

## Validations numériques : flottants, supérieur et inférieur

Les validations numériques fonctionnent également pour les valeurs `float`.

Валидация также применима к значениям типа `float`.

В этом случае становится важной возможность добавить ограничение <abbr title="greater than"><code>gt</code></abbr>, вместо <abbr title="greater than or equal"><code>ge</code></abbr>, поскольку в таком случае вы можете, например, создать ограничение, чтобы значение было больше `0`, даже если оно меньше `1`.

```

## 숫자 검증: 부동소수, 크거나 및 작거나

숫자 검증은 `float` 값에도 동작합니다.

여기에서 <abbr title="greater than or equal"><code>ge</code></abbr>뿐만 아니라 <abbr title="greater than"><code>gt</code></abbr>를 선언 할 수있는 것이 중요해집니다. 예를 들어 필요한 경우, 값이 `1`보다 작더라도 반드시 `0`보다 커야합니다.

즉, `0.5`는 유효한 값입니다. 그러나 `0.0` 또는 `0`은 그렇지 않습니다.

<abbr title="less than"><code>lt</code></abbr> 역시 마찬가지입니다.

```Python hl_lines="11"

Zahlenvalidierung funktioniert auch für <abbr title="Kommazahl">`float`</abbr>-Werte.

Hier wird es wichtig, in der Lage zu sein, <abbr title="greater than – größer als"><code>gt</code></abbr> zu deklarieren, und nicht nur <abbr title="greater than or equal – größer oder gleich"><code>ge</code></abbr>, da Sie hiermit bestimmen können, dass ein Wert, zum Beispiel, größer als `0` sein muss, obwohl er kleiner als `1` ist.

 * @author Louis Wasserman
 * @since 2.0
 */
@GwtCompatible(emulated = true)
@ElementTypesAreNonnullByDefault
public final class Lists {
  private Lists() {}

  // ArrayList

  /**
   * Creates a <i>mutable</i>, empty {@code ArrayList} instance (for Java 6 and earlier).
   *
   * <p><b>Note:</b> if mutability is not required, use {@link ImmutableList#of()} instead.
   *

  // TODO(user): cache all field accesses in local vars

  /** Creates an empty {@code CompactHashSet} instance. */
  public static <E extends @Nullable Object> CompactHashSet<E> create() {
    return new CompactHashSet<>();
  }

  /**
   * Creates a <i>mutable</i> {@code CompactHashSet} instance containing the elements of the given
   * collection in unspecified order.
   *

   * @return the value with the specified row and column
   * @throws IndexOutOfBoundsException if either index is negative, {@code rowIndex} is greater than
   *     or equal to the number of allowed row keys, or {@code columnIndex} is greater than or equal
   *     to the number of allowed column keys
   */
  @CheckForNull
  public V at(int rowIndex, int columnIndex) {

   * minimum hashtable size, whichever is greater.
   */
  static int tableSize(int expectedSize) {
    // We use entries next == 0 to indicate UNSET, so actual capacity is 1 less than requested.
    return max(MIN_HASH_TABLE_SIZE, Hashing.closedTableSize(expectedSize + 1, 1.0));
  }

  /** Creates and returns a properly-sized array with the given number of buckets. */