## Number validations: greater than and less than or equal { #number-validations-greater-than-and-less-than-or-equal }

The same applies for:

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

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

## Number validations: floats, greater than and less than { #number-validations-floats-greater-than-and-less-than }

## Валідація числових даних: float, більше ніж і менше ніж

Валідація чисел також працює для значень типу `float`.

Ось де стає важливо мати можливість оголошувати <abbr title="greater than (більше ніж)"><code>gt</code></abbr>, а не тільки <abbr title="greater than or equal (більше або дорівнює)"><code>ge</code></abbr>. Це дозволяє, наприклад, вимагати, щоб значення було більше `0`, навіть якщо воно менше `1`.

      assertTrue(t.equals(t));

      for (int j = i + 1; j < valuesInExpectedOrder.size(); j++) {
        T greater = valuesInExpectedOrder.get(j);
        assertTrue(greater + ".compareTo(" + t + ')', greater.compareTo(t) > 0);
        assertFalse(greater.equals(t));
      }
    }
  }

  /**
   * Returns a collection that simulates concurrent modification by having its size method return

        assertTrue(Modifier.isPrivate(constructor.getModifiers()), "Constructor should be private");

        // Force accessibility and create instance to achieve coverage
        constructor.setAccessible(true);
        assertNotNull(constructor.newInstance(), "Should be able to create instance via reflection");
    }

    @Nested
    @DisplayName("Header Constants")
    class HeaderConstants {

        @Test

    }

    /**
     * Tests the constructor with a byte array that is larger than the minimal buffer size.
     */
    @Test
    void testConstructorWithDataMuchLarger() {
        // A byte array with a length greater than 32 should also be considered too large.
        byte[] veryLargeData = new byte[100];
        PACDecodingException exception = assertThrows(PACDecodingException.class, () -> new PacCredentialType(veryLargeData));

   */
  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>
   *

     */
    public FacetResponse getFacetResponse() {
        return facetResponse;
    }

    /**
     * Creates a new SearchResultBuilder for constructing SearchResult instances.
     *
     * @return A new SearchResultBuilder instance
     */
    public static SearchResultBuilder create() {
        return new SearchResultBuilder();
    }

    @Override
    public String toString() {

    IndexOutOfBoundsException expected =
        assertThrows(IndexOutOfBoundsException.class, () -> checkPositionIndex(2, 1));
    assertThat(expected).hasMessageThat().isEqualTo("index (2) must not be greater than size (1)");
  }

  public void testCheckPositionIndex_withDesc_negative() {
    IndexOutOfBoundsException expected =
        assertThrows(IndexOutOfBoundsException.class, () -> checkPositionIndex(-1, 1, "foo"));

    IndexOutOfBoundsException expected =
        assertThrows(IndexOutOfBoundsException.class, () -> checkPositionIndex(2, 1));
    assertThat(expected).hasMessageThat().isEqualTo("index (2) must not be greater than size (1)");
  }

  public void testCheckPositionIndex_withDesc_negative() {
    IndexOutOfBoundsException expected =
        assertThrows(IndexOutOfBoundsException.class, () -> checkPositionIndex(-1, 1, "foo"));

   * Compares the two specified {@code double} values. The sign of the value returned is the same as
   * that of <code>((Double) a).{@linkplain Double#compareTo compareTo}(b)</code>. As with that
   * method, {@code NaN} is treated as greater than all other values, and {@code 0.0 > -0.0}.
   *
   * <p><b>Note:</b> this method simply delegates to the JDK method {@link Double#compare}. It is