```Python hl_lines="9"
{!../../docs_src/path_params_numeric_validations/tutorial005.py!}
```

## 🔢 🔬: 🎈, 🌘 🌘 & 🌘 🌘

🔢 🔬 👷 `float` 💲.

📥 🌐❔ ⚫️ ▶️️ ⚠ 💪 📣 <abbr title="greater than"><code>gt</code></abbr> &amp; 🚫 <abbr title="greater than or equal"><code>ge</code></abbr>. ⏮️ ⚫️ 👆 💪 🚚, 🖼, 👈 💲 🔜 👑 🌘 `0`, 🚥 ⚫️ 🌘 🌘 `1`.

, `0.5` 🔜 ☑ 💲. ✋️ `0.0` ⚖️ `0` 🔜 🚫.

&amp; 🎏 <abbr title="less than"><code>lt</code></abbr>.

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`.

 *
 * <ol>
 *   <li>First, if only one {@code Foo} is null, that null value is treated as <i>greater</i>
 *   <li>Next, non-null {@code Foo} values are passed to {@code getBarFunction} (we will be
 *       comparing {@code Bar} values from now on)
 *   <li>Next, if only one {@code Bar} is null, that null value is treated as <i>lesser</i>
 *   <li>Finally, natural ordering is used (i.e. the result of {@code Bar.compareTo(Bar)} is

	Credentials auth.Credentials `xml:",omitempty"`

	// A percentage value that indicates the size of the policy in packed form.
	// The service rejects any policy with a packed size greater than 100 percent,
	// which means the policy exceeded the allowed space.
	PackedPolicySize int `xml:",omitempty"`
}

// AssumeRoleWithWebIdentityResponse contains the result of successful AssumeRoleWithWebIdentity request.

   */
  public double populationCovariance() {
    checkState(count() != 0);
    return sumOfProductsOfDeltas / count();
  }

  /**
   * Returns the sample covariance of the values. The count must be greater than one.
   *
   * <p>This is not guaranteed to return zero when the dataset consists of the same pair of values
   * multiple times, due to numerical errors.
   *
   * <h3>Non-finite values</h3>
   *

class Item(BaseModel):
    name: str
    description: str | None = Field(
        default=None, title="The description of the item", max_length=300
    )
    price: float = Field(gt=0, description="The price must be greater than zero")
    tax: float | None = None


@app.put("/items/{item_id}")
async def update_item(item_id: int, item: Item = Body(embed=True)):
    results = {"item_id": item_id, "item": item}

                    },
                    {
                        "type": "greater_than_equal",
                        "loc": ["query", "offset"],
                        "msg": "Input should be greater than or equal to 0",
                        "input": "-1",
                        "ctx": {"ge": 0},
                    },
                    {
                        "type": "literal_error",

class Item(BaseModel):
    name: str
    description: Union[str, None] = Field(
        default=None, title="The description of the item", max_length=300
    )
    price: float = Field(gt=0, description="The price must be greater than zero")
    tax: Union[float, None] = None


@app.put("/items/{item_id}")
async def update_item(item_id: int, item: Item = Body(embed=True)):
    results = {"item_id": item_id, "item": item}

class Item(BaseModel):
    name: str
    description: Union[str, None] = Field(
        default=None, title="The description of the item", max_length=300
    )
    price: float = Field(gt=0, description="The price must be greater than zero")
    tax: Union[float, None] = None


@app.put("/items/{item_id}")
async def update_item(item_id: int, item: Annotated[Item, Body(embed=True)]):
    results = {"item_id": item_id, "item": item}