Тут, завдяки `ge=1`, `item_id` має бути цілим числом, яке "`g`reater than or `e`qual" (більше або дорівнює) `1`.

{* ../../docs_src/path_params_numeric_validations/tutorial004_an_py39.py hl[10] *}

## Валідація числових даних: більше ніж і менше або дорівнює

Те саме застосовується до:

* `gt`: `g`reater `t`han (більше ніж)
* `le`: `l`ess than or `e`qual (менше або дорівнює)

 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

// it under the terms of the GNU Affero General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

// it under the terms of the GNU Affero General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

### Threads

#### Application's calling thread

The application-layer must block on writing I/O. We can't return from a write until we've pushed its bytes onto the socket. Otherwise, if the write fails we are unable to deliver its IOException to the application. We would have told the application layer that the write succeeded, but it didn't!

    double hit = req - misses.get();

    // Currently, this is going into /dev/null, but I'll fix that
    System.out.println("hit rate: " + hit / req);
  }

  // for proper distributions later:
  // import JSci.maths.statistics.ProbabilityDistribution;
  // int key = (int) dist.inverse(random.nextDouble());

{* ../../docs_src/dependencies/tutorial006_an_py39.py hl[11,16] *}

## Dependencies for a group of *path operations* { #dependencies-for-a-group-of-path-operations }