checkRoundingUnnecessary(sqrtFloor.pow(2).equals(x)); // fall through
      case FLOOR:
      case DOWN:
        return sqrtFloor;
      case CEILING:
      case UP:
        int sqrtFloorInt = sqrtFloor.intValue();
        boolean sqrtFloorIsExact =
            (sqrtFloorInt * sqrtFloorInt == x.intValue()) // fast check mod 2^32
                && sqrtFloor.pow(2).equals(x); // slow exact check

   * array as the lesser. For example, {@code [] < ['a'] < ['a', 'b'] < ['b']}.
   *
   * <p>The returned comparator is inconsistent with {@link Object#equals(Object)} (since arrays
   * support only identity equality), but it is consistent with {@link Arrays#equals(char[],
   * char[])}.
   *
   * @since 2.0
   */
  public static Comparator<char[]> lexicographicalComparator() {

      monitor.leave();
    }
  }

  /**
   * Removes a single instance of the specified element from this queue, if it is present. More
   * formally, removes an element {@code e} such that {@code o.equals(e)}, if this queue contains
   * one or more such elements. Returns {@code true} if this queue contained the specified element
   * (or equivalently, if this queue changed as a result of the call).
   *

  public int hashCode() {
    return -forwardOrder.hashCode();
  }

  @Override
  public boolean equals(@CheckForNull Object object) {
    if (object == this) {
      return true;
    }
    if (object instanceof ReverseOrdering) {
      ReverseOrdering<?> that = (ReverseOrdering<?>) object;
      return this.forwardOrder.equals(that.forwardOrder);
    }
    return false;
  }

  @Override

import com.google.common.testing.EqualsTester;
import java.util.ArrayList;
import java.util.List;
import java.util.Map.Entry;
import org.checkerframework.checker.nullness.qual.Nullable;
import org.junit.Ignore;

/**
 * Tester for {@code Multimap.equals}.
 *
 * @author Louis Wasserman
 */
@GwtCompatible
@Ignore // Affects only Android test runner, which respects JUnit 4 annotations on JUnit 3 tests.

{!> ../../docs_src/path_params_numeric_validations/tutorial003_an.py!}
```

////

## Number validations: greater than or equal

With `Query` and `Path` (and others you'll see later) you can declare number constraints.

Here, with `ge=1`, `item_id` will need to be an integer number "`g`reater than or `e`qual" to `1`.

//// tab | Python 3.9+

```Python hl_lines="10"

   * example, {@code [] < [1] < [1, 2] < [2]}.
   *
   * <p>The returned comparator is inconsistent with {@link Object#equals(Object)} (since arrays
   * support only identity equality), but it is consistent with {@link Arrays#equals(int[], int[])}.
   *
   * @since 2.0
   */
  public static Comparator<int[]> lexicographicalComparator() {
    return LexicographicalComparator.INSTANCE;
  }

    return Integer.MAX_VALUE;
  }

  /**
   * Removes a single instance of the specified element from this queue, if it is present. More
   * formally, removes an element {@code e} such that {@code o.equals(e)}, if this queue contains
   * one or more such elements. Returns {@code true} if and only if this queue contained the
   * specified element (or equivalently, if this queue changed as a result of the call).
   *

  }

  @Override
  public final boolean equals(@CheckForNull Object obj) {
    if (obj instanceof Subscriber) {
      Subscriber that = (Subscriber) obj;
      // Use == so that different equal instances will still receive events.
      // We only guard against the case that the same object is registered
      // multiple times
      return target == that.target && method.equals(that.method);
    }
    return false;
  }

    @Override
    public boolean equals(@CheckForNull Object obj) {
      if (obj == this) {
        return true;
      }
      if (obj instanceof Cell) {
        Cell<?, ?, ?> other = (Cell<?, ?, ?>) obj;
        return Objects.equal(getRowKey(), other.getRowKey())
            && Objects.equal(getColumnKey(), other.getColumnKey())
            && Objects.equal(getValue(), other.getValue());
      }