동일하게 적용됩니다:

* `gt`: 크거나(`g`reater `t`han)
* `le`: 작거나 같은(`l`ess than or `e`qual)

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

## 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.

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}

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: Annotated[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}

I have been avoiding the creation of a new framework for several years. First I tried to solve all the features covered by **FastAPI** using many different frameworks, plug-ins, and tools.

But at some point, there was no other option than creating something that provided all these features, taking the best ideas from previous tools, and combining them in the best way possible, using language features that weren't even available before (Python 3.6+ type hints).

## Changing the default

When you run `fastapi dev`, it will run on development mode.

By default, it will have **auto-reload** enabled, so it will automatically reload the server when you make changes to your code. This is resource intensive and could be less stable than without it, you should only use it for development.

By default it will listen on the IP address `127.0.0.1`, which is the IP for your machine to communicate with itself alone (`localhost`).

## `fastapi run`

# Extra Models

Continuing with the previous example, it will be common to have more than one related model.

This is especially the case for user models, because:

* The **input model** needs to be able to have a password.
* The **output model** should not have a password.
* The **database model** would probably need to have a hashed password.

!!! danger
    Never store user's plaintext passwords. Always store a "secure hash" that you can then verify.

```

### Declare a `list` with a type parameter

To declare types that have type parameters (internal types), like `list`, `dict`, `tuple`:

* If you are in a Python version lower than 3.9, import their equivalent version from the `typing` module
* Pass the internal type(s) as "type parameters" using square brackets: `[` and `]`

In Python 3.9 it would be:

```Python
my_list: list[str]
```

Because `Annotated` can have more than one metadata annotation, you could now even use the same function with other tools, like <a href="https://typer.tiangolo.com/" class="external-link" target="_blank">Typer</a>. 🚀

## Add more validations