diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index b5900ead246f3..7827cd9bfe332 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -5523,6 +5523,17 @@ def _cmp_method(self, other, op):
         """
         Wrapper used to dispatch comparison operations.
         """
+        if self.is_(other):
+            # fastpath
+            if op in {operator.eq, operator.le, operator.ge}:
+                arr = np.ones(len(self), dtype=bool)
+                if self._can_hold_na and not isinstance(self, ABCMultiIndex):
+                    # TODO: should set MultiIndex._can_hold_na = False?
+                    arr[self.isna()] = False
+                return arr
+            elif op in {operator.ne, operator.lt, operator.gt}:
+                return np.zeros(len(self), dtype=bool)
+
         if isinstance(other, (np.ndarray, Index, ABCSeries, ExtensionArray)):
             if len(self) != len(other):
                 raise ValueError("Lengths must match to compare")
diff --git a/pandas/core/indexes/numeric.py b/pandas/core/indexes/numeric.py
index 7778b1e264cd8..8a1bcc7146616 100644
--- a/pandas/core/indexes/numeric.py
+++ b/pandas/core/indexes/numeric.py
@@ -1,4 +1,3 @@
-import operator
 from typing import Any
 import warnings
 
@@ -6,7 +5,7 @@
 
 from pandas._libs import index as libindex, lib
 from pandas._typing import Dtype, Label
-from pandas.util._decorators import cache_readonly, doc
+from pandas.util._decorators import doc
 
 from pandas.core.dtypes.cast import astype_nansafe
 from pandas.core.dtypes.common import (
@@ -188,18 +187,6 @@ def _union(self, other, sort):
         else:
             return super()._union(other, sort)
 
-    def _cmp_method(self, other, op):
-        if self.is_(other):  # fastpath
-            if op in {operator.eq, operator.le, operator.ge}:
-                arr = np.ones(len(self), dtype=bool)
-                if self._can_hold_na:
-                    arr[self.isna()] = False
-                return arr
-            elif op in {operator.ne, operator.lt, operator.gt}:
-                return np.zeros(len(self), dtype=bool)
-
-        return super()._cmp_method(other, op)
-
 
 _num_index_shared_docs[
     "class_descr"
@@ -243,6 +230,20 @@ class IntegerIndex(NumericIndex):
     """
 
     _default_dtype: np.dtype
+    _can_hold_na = False
+
+    @classmethod
+    def _assert_safe_casting(cls, data, subarr):
+        """
+        Ensure incoming data can be represented with matching signed-ness.
+        """
+        if data.dtype.kind != cls._default_dtype.kind:
+            if not np.array_equal(data, subarr):
+                raise TypeError("Unsafe NumPy casting, you must explicitly cast")
+
+    def _can_union_without_object_cast(self, other) -> bool:
+        # See GH#26778, further casting may occur in NumericIndex._union
+        return other.dtype == "f8" or other.dtype == self.dtype
 
     def __contains__(self, key) -> bool:
         """
@@ -278,23 +279,9 @@ class Int64Index(IntegerIndex):
     __doc__ = _num_index_shared_docs["class_descr"] % _int64_descr_args
 
     _typ = "int64index"
-    _can_hold_na = False
     _engine_type = libindex.Int64Engine
     _default_dtype = np.dtype(np.int64)
 
-    @classmethod
-    def _assert_safe_casting(cls, data, subarr):
-        """
-        Ensure incoming data can be represented as ints.
-        """
-        if not issubclass(data.dtype.type, np.signedinteger):
-            if not np.array_equal(data, subarr):
-                raise TypeError("Unsafe NumPy casting, you must explicitly cast")
-
-    def _can_union_without_object_cast(self, other) -> bool:
-        # See GH#26778, further casting may occur in NumericIndex._union
-        return other.dtype == "f8" or other.dtype == self.dtype
-
 
 _uint64_descr_args = dict(
     klass="UInt64Index", ltype="unsigned integer", dtype="uint64", extra=""
@@ -305,7 +292,6 @@ class UInt64Index(IntegerIndex):
     __doc__ = _num_index_shared_docs["class_descr"] % _uint64_descr_args
 
     _typ = "uint64index"
-    _can_hold_na = False
     _engine_type = libindex.UInt64Engine
     _default_dtype = np.dtype(np.uint64)
 
@@ -324,21 +310,6 @@ def _convert_arr_indexer(self, keyarr):
 
         return com.asarray_tuplesafe(keyarr, dtype=dtype)
 
-    # ----------------------------------------------------------------
-
-    @classmethod
-    def _assert_safe_casting(cls, data, subarr):
-        """
-        Ensure incoming data can be represented as uints.
-        """
-        if not issubclass(data.dtype.type, np.unsignedinteger):
-            if not np.array_equal(data, subarr):
-                raise TypeError("Unsafe NumPy casting, you must explicitly cast")
-
-    def _can_union_without_object_cast(self, other) -> bool:
-        # See GH#26778, further casting may occur in NumericIndex._union
-        return other.dtype == "f8" or other.dtype == self.dtype
-
 
 _float64_descr_args = dict(
     klass="Float64Index", dtype="float64", ltype="float", extra=""
@@ -350,7 +321,7 @@ class Float64Index(NumericIndex):
 
     _typ = "float64index"
     _engine_type = libindex.Float64Engine
-    _default_dtype = np.float64
+    _default_dtype = np.dtype(np.float64)
 
     @property
     def inferred_type(self) -> str:
@@ -429,10 +400,6 @@ def __contains__(self, other: Any) -> bool:
 
         return is_float(other) and np.isnan(other) and self.hasnans
 
-    @cache_readonly
-    def is_unique(self) -> bool:
-        return super().is_unique and self._nan_idxs.size < 2
-
     def _can_union_without_object_cast(self, other) -> bool:
         # See GH#26778, further casting may occur in NumericIndex._union
         return is_numeric_dtype(other.dtype)