diff --git a/mathics/builtin/atomic/strings.py b/mathics/builtin/atomic/strings.py
index 22291b7ec..3fe7a5582 100644
--- a/mathics/builtin/atomic/strings.py
+++ b/mathics/builtin/atomic/strings.py
@@ -616,9 +616,6 @@ class _StringFind(Builtin, ABC):
 
     messages = {
         "srep": "`1` is not a valid string replacement rule.",
-        "innf": (
-            "Non-negative integer or Infinity expected at " "position `1` in `2`."
-        ),
     }
 
     def _find(py_stri, py_rules, py_n, flags):
diff --git a/mathics/builtin/list/eol.py b/mathics/builtin/list/eol.py
index bce7422ab..1eef7990f 100644
--- a/mathics/builtin/list/eol.py
+++ b/mathics/builtin/list/eol.py
@@ -8,10 +8,9 @@
 """
 
 from itertools import chain
-from typing import Optional
 
 from mathics.builtin.box.layout import RowBox
-from mathics.core.atoms import Integer, Integer0, Integer1, String
+from mathics.core.atoms import Integer, Integer0, Integer1, Integer3, Integer4, String
 from mathics.core.attributes import (
     A_HOLD_FIRST,
     A_HOLD_REST,
@@ -30,7 +29,7 @@
     PartError,
     PartRangeError,
 )
-from mathics.core.expression import Expression
+from mathics.core.expression import Expression, ExpressionInfinity
 from mathics.core.list import ListExpression
 from mathics.core.rules import Rule
 from mathics.core.symbols import Atom, Symbol, SymbolNull, SymbolTrue
@@ -42,6 +41,7 @@
     SymbolKey,
     SymbolMakeBoxes,
     SymbolMissing,
+    SymbolSelect,
     SymbolSequence,
     SymbolSet,
 )
@@ -437,7 +437,6 @@ class DeleteCases(Builtin):
 
     messages = {
         "level": "Level specification `1` is not of the form n, {n}, or {m, n}.",
-        "innf": "Non-negative integer or Infinity expected at position 4 in `1`",
     }
     summary_text = "delete all occurrences of a pattern"
 
@@ -455,14 +454,15 @@ def eval_ls_n(self, items, pattern, levelspec, n, evaluation):
 
         levelspec = python_levelspec(levelspec)
 
-        if n is SymbolInfinity:
+        if n is SymbolInfinity or ExpressionInfinity == n:
             n = -1
-        elif n.get_head_name() == "System`Integer":
-            n = n.get_int_value()
+        elif isinstance(n, Integer):
+            n = n.value
             if n < 0:
                 evaluation.message(
                     "DeleteCases",
                     "innf",
+                    Integer4,
                     Expression(SymbolDeleteCases, items, pattern, levelspec, n),
                 )
         else:
@@ -1533,10 +1533,26 @@ class Select(Builtin):
     def eval(self, items, expr, evaluation: Evaluation):
         "Select[items_, expr_]"
 
-        return self.eval_with_n(items, expr, None, evaluation)
+        return self.eval_with_n(items, expr, SymbolInfinity, evaluation)
 
-    def eval_with_n(self, items, expr, n: Optional[Integer], evaluation: Evaluation):
-        "Select[items_, expr_, n_Integer]"
+    def eval_with_n(self, items, expr, n, evaluation: Evaluation):
+        "Select[items_, expr_, n_]"
+
+        count_is_valid = True
+        if n is SymbolInfinity or ExpressionInfinity == n:
+            count = None
+        elif isinstance(n, Integer):
+            count = n.value
+            if count < 0:
+                count_is_valid = False
+        else:
+            count_is_valid = False
+
+        if not count_is_valid:
+            evaluation.message(
+                "Select", "innf", Integer3, Expression(SymbolSelect, items, expr, n)
+            )
+            return
 
         if isinstance(items, Atom):
             evaluation.message("Select", "normal")
@@ -1546,7 +1562,6 @@ def cond(element):
             test = Expression(expr, element)
             return test.evaluate(evaluation) is SymbolTrue
 
-        count = n.value if n is not None else None
         return items.filter(items.head, cond, evaluation, count=count)
 
 
@@ -1633,6 +1648,7 @@ class UpTo(Builtin):
     </dl>
     """
 
+    # TODO: is there as way we can use general's innf?
     messages = {
         "innf": "Expected non-negative integer or infinity at position 1 in ``.",
         "argx": "UpTo expects 1 argument, `1` arguments were given.",
diff --git a/mathics/builtin/messages.py b/mathics/builtin/messages.py
index 31dc48d38..e926ab001 100644
--- a/mathics/builtin/messages.py
+++ b/mathics/builtin/messages.py
@@ -198,7 +198,7 @@ class General(Builtin):
             "Single or list of non-negative integers expected at " "position `1`."
         ),
         "indet": "Indeterminate expression `1` encountered.",
-        "innf": "Non-negative integer or Infinity expected at position `1`.",
+        "innf": "Non-negative integer or Infinity expected at position `1` in `2`",
         "int": "Integer expected.",
         "intp": "Positive integer expected.",
         "intnn": "Non-negative integer expected.",
diff --git a/mathics/builtin/patterns/rules.py b/mathics/builtin/patterns/rules.py
index 2055f305a..b95aab8ef 100644
--- a/mathics/builtin/patterns/rules.py
+++ b/mathics/builtin/patterns/rules.py
@@ -69,16 +69,21 @@
 
 from typing import Optional as OptionalType
 
-from mathics.core.atoms import Integer, Integer0, Integer2, Number
+from mathics.core.atoms import Integer, Integer0, Integer2, Integer3, Number
 from mathics.core.attributes import A_HOLD_REST, A_PROTECTED, A_SEQUENCE_HOLD
 from mathics.core.builtin import AtomBuiltin, Builtin, InfixOperator, PatternError
 from mathics.core.element import BaseElement
 from mathics.core.evaluation import Evaluation
 from mathics.core.exceptions import InvalidLevelspecError
-from mathics.core.expression import Expression
+from mathics.core.expression import Expression, ExpressionInfinity
 from mathics.core.list import ListExpression
 from mathics.core.symbols import SymbolTrue
-from mathics.core.systemsymbols import SymbolInfinity, SymbolRule, SymbolRuleDelayed
+from mathics.core.systemsymbols import (
+    SymbolInfinity,
+    SymbolReplaceList,
+    SymbolRule,
+    SymbolRuleDelayed,
+)
 from mathics.eval.rules import (
     Dispatch,
     create_rules,
@@ -341,9 +346,6 @@ class ReplaceList(Builtin):
     Like in 'ReplaceAll', $rules$ can be a nested list:
     >> ReplaceList[{a, b, c}, {{{___, x__, ___} -> {x}}, {{a, b, c} -> t}}, 2]
      = {{{a}, {a, b}}, {t}}
-    >> ReplaceList[expr, {}, -1]
-     : Non-negative integer or Infinity expected at position 3.
-     = ReplaceList[expr, {}, -1]
 
     Possible matches for a sum:
     >> ReplaceList[a + b + c, x_ + y_ -> {x, y}]
@@ -369,12 +371,17 @@ def eval(
         # default argument, when it is passed explictly, e.g.
         # ReplaceList[expr, {}, Infinity], then Infinity
         # comes in as DirectedInfinity[1].
-        if maxidx == SymbolInfinity:
+        if maxidx == SymbolInfinity or ExpressionInfinity == maxidx:
             max_count = None
         else:
             max_count = maxidx.get_int_value()
             if max_count is None or max_count < 0:
-                evaluation.message("ReplaceList", "innf", 3)
+                evaluation.message(
+                    "ReplaceList",
+                    "innf",
+                    Integer3,
+                    Expression(SymbolReplaceList, expr, rules, maxidx),
+                )
                 return None
         try:
             rules, ret = create_rules(
diff --git a/mathics/builtin/scipy_utils/optimizers.py b/mathics/builtin/scipy_utils/optimizers.py
index a704b9596..4d705255e 100644
--- a/mathics/builtin/scipy_utils/optimizers.py
+++ b/mathics/builtin/scipy_utils/optimizers.py
@@ -6,8 +6,8 @@
 from mathics.core.convert.function import expression_to_callable_and_args
 from mathics.core.element import BaseElement
 from mathics.core.evaluation import Evaluation
-from mathics.core.expression import Expression
-from mathics.core.systemsymbols import SymbolAutomatic, SymbolFailed, SymbolInfinity
+from mathics.core.expression import Expression, ExpressionInfinity
+from mathics.core.systemsymbols import SymbolAutomatic, SymbolFailed
 from mathics.eval.nevaluator import eval_N
 
 if not check_requires_list(["scipy", "numpy"]):
@@ -30,7 +30,7 @@ def get_tolerance_and_maxit(opts: dict, scale: float, evaluation: Evaluation):
         acc_goal = eval_N(acc_goal, evaluation)
         if acc_goal is SymbolAutomatic:
             acc_goal = Real(12.0)
-        elif acc_goal is SymbolInfinity:
+        elif ExpressionInfinity == acc_goal:
             acc_goal = None
         elif not isinstance(acc_goal, Number):
             acc_goal = None
@@ -40,7 +40,7 @@ def get_tolerance_and_maxit(opts: dict, scale: float, evaluation: Evaluation):
         prec_goal = eval_N(prec_goal, evaluation)
         if prec_goal is SymbolAutomatic:
             prec_goal = Real(12.0)
-        elif prec_goal is SymbolInfinity:
+        elif ExpressionInfinity == prec_goal:
             prec_goal = None
         elif not isinstance(prec_goal, Number):
             prec_goal = None
diff --git a/mathics/builtin/string/operations.py b/mathics/builtin/string/operations.py
index 99aeff2ca..ac294c3fd 100644
--- a/mathics/builtin/string/operations.py
+++ b/mathics/builtin/string/operations.py
@@ -13,7 +13,7 @@
     mathics_split,
     to_regex,
 )
-from mathics.core.atoms import Integer, Integer1, String
+from mathics.core.atoms import Integer, Integer1, Integer3, String
 from mathics.core.attributes import (
     A_FLAT,
     A_LISTABLE,
@@ -437,7 +437,7 @@ def eval_n(self, string, patt, n, evaluation: Evaluation, options: dict):
         else:
             py_n = n.get_int_value()
             if py_n is None or py_n < 0:
-                evaluation.message("StringPosition", "innf", expr, Integer(3))
+                evaluation.message("StringPosition", "innf", expr, Integer3)
                 return
 
         # check options
diff --git a/mathics/core/atoms.py b/mathics/core/atoms.py
index ad98756bc..2ee59657b 100644
--- a/mathics/core/atoms.py
+++ b/mathics/core/atoms.py
@@ -329,6 +329,7 @@ def is_zero(self) -> bool:
 Integer1 = Integer(1)
 Integer2 = Integer(2)
 Integer3 = Integer(3)
+Integer4 = Integer(4)
 Integer310 = Integer(310)
 Integer10 = Integer(10)
 IntegerM1 = Integer(-1)
diff --git a/mathics/core/expression.py b/mathics/core/expression.py
index 2910491f5..c1560db95 100644
--- a/mathics/core/expression.py
+++ b/mathics/core/expression.py
@@ -19,7 +19,7 @@
 
 import sympy
 
-from mathics.core.atoms import Integer, String
+from mathics.core.atoms import Integer, Integer1, String
 from mathics.core.attributes import (
     A_FLAT,
     A_HOLD_ALL,
@@ -2068,3 +2068,6 @@ def convert_expression_elements(
 
 def string_list(head, elements, evaluation):
     return atom_list_constructor(evaluation, head, "String")(elements)
+
+
+ExpressionInfinity = Expression(SymbolDirectedInfinity, Integer1)
diff --git a/mathics/core/systemsymbols.py b/mathics/core/systemsymbols.py
index 892763bd0..1798a9bb8 100644
--- a/mathics/core/systemsymbols.py
+++ b/mathics/core/systemsymbols.py
@@ -216,6 +216,7 @@
 SymbolRealSign = Symbol("System`RealSign")
 SymbolRepeated = Symbol("System`Repeated")
 SymbolRepeatedNull = Symbol("System`RepeatedNull")
+SymbolReplaceList = Symbol("System`ReplaceList")
 SymbolReturn = Symbol("System`Return")
 SymbolReverse = Symbol("System`Reverse")
 SymbolRight = Symbol("System`Right")
@@ -225,6 +226,7 @@
 SymbolRule = Symbol("System`Rule")
 SymbolRuleDelayed = Symbol("System`RuleDelayed")
 SymbolSameQ = Symbol("System`SameQ")
+SymbolSelect = Symbol("System`Select")
 SymbolSequence = Symbol("System`Sequence")
 SymbolSeries = Symbol("System`Series")
 SymbolSeriesData = Symbol("System`SeriesData")
diff --git a/mathics/eval/numbers/calculus/optimizers.py b/mathics/eval/numbers/calculus/optimizers.py
index 4798f1362..01178af5e 100644
--- a/mathics/eval/numbers/calculus/optimizers.py
+++ b/mathics/eval/numbers/calculus/optimizers.py
@@ -19,7 +19,7 @@
 )
 from mathics.core.convert.python import from_python
 from mathics.core.evaluation import Evaluation
-from mathics.core.expression import Expression
+from mathics.core.expression import Expression, ExpressionInfinity
 from mathics.core.symbols import BaseElement, SymbolPlus, SymbolTimes, SymbolTrue
 from mathics.core.systemsymbols import (
     SymbolAutomatic,
@@ -431,7 +431,7 @@ def to_real_or_none(value) -> Optional[Real]:
             value = eval_N(value, evaluation)
         if value is SymbolAutomatic:
             value = Real(12.0)
-        elif value is SymbolInfinity:
+        elif value is SymbolInfinity or ExpressionInfinity == value:
             value = None
         elif not isinstance(value, Number):
             value = None
@@ -442,7 +442,7 @@ def to_integer_or_none(value) -> Optional[Integer]:
             value = eval_N(value, evaluation)
         if value is SymbolAutomatic:
             value = Integer(100)
-        elif value is SymbolInfinity:
+        elif value is SymbolInfinity or ExpressionInfinity == value:
             value = None
         elif not isinstance(value, Number):
             value = None
diff --git a/test/builtin/list/test_eol.py b/test/builtin/list/test_eol.py
index 869bc3bcc..8ae460746 100644
--- a/test/builtin/list/test_eol.py
+++ b/test/builtin/list/test_eol.py
@@ -226,6 +226,7 @@
         ## Formatting
         ("a ;; b ;; c", None, "a ;; b ;; c", None),
         ("a ;; b", None, "a ;; b", None),
+        # TODO: Rework this test
         ("{a ;; b ;; c ;; d}", None, "{a ;; b ;; c, 1 ;; d}", ";; association"),
         (
             "Select[a, True]",
@@ -233,7 +234,6 @@
             "Select[a, True]",
             None,
         ),
-        # TODO: Rework this test
         ("Take[Range[10], {8, 2, -1}]", None, "{8, 7, 6, 5, 4, 3, 2}", None),
         ("Take[Range[10], {-3, -7, -2}]", None, "{8, 6, 4}", None),
         (