diff --git a/src/sage/geometry/fan_morphism.py b/src/sage/geometry/fan_morphism.py
index 7ef46b80d17..5a8aef777f8 100644
--- a/src/sage/geometry/fan_morphism.py
+++ b/src/sage/geometry/fan_morphism.py
@@ -89,7 +89,7 @@
 from sage.modules.free_module_morphism import FreeModuleMorphism
 from sage.rings.infinity import Infinity
 from sage.rings.integer_ring import ZZ
-from sage.rings.infinity import is_Infinite
+from sage.rings.infinity import InfinityElement
 from functools import reduce
 
 
@@ -1458,7 +1458,7 @@ def is_surjective(self):
             sage: phi.is_surjective()
             False
         """
-        if is_Infinite(self.index()):
+        if isinstance(self.index(), InfinityElement):
             return False    # Not surjective between vector spaces.
         for dcones in self.codomain_fan().cones():
             for sigma_p in dcones:
diff --git a/src/sage/modular/arithgroup/arithgroup_element.pyx b/src/sage/modular/arithgroup/arithgroup_element.pyx
index 6bcd2c58550..db914af629b 100644
--- a/src/sage/modular/arithgroup/arithgroup_element.pyx
+++ b/src/sage/modular/arithgroup/arithgroup_element.pyx
@@ -375,8 +375,8 @@ cdef class ArithmeticSubgroupElement(MultiplicativeGroupElement):
             sage: G([1, 4, 0, 1]).acton(infinity)
             +Infinity
         """
-        from sage.rings.infinity import is_Infinite, infinity
-        if is_Infinite(z):
+        from sage.rings.infinity import InfinityElement, infinity
+        if isinstance(z, InfinityElement):
             if self.c() != 0:
                 return self.a() / self.c()
             else:
diff --git a/src/sage/rings/infinity.py b/src/sage/rings/infinity.py
index 182b2dd8b8d..16826c872ce 100644
--- a/src/sage/rings/infinity.py
+++ b/src/sage/rings/infinity.py
@@ -976,6 +976,10 @@ def is_Infinite(x) -> bool:
     EXAMPLES::
 
         sage: sage.rings.infinity.is_Infinite(oo)
+        doctest:warning...
+        DeprecationWarning: The function is_Infinite is deprecated;
+        use 'isinstance(..., InfinityElement)' instead.
+        See https://github.com/sagemath/sage/issues/38022 for details.
         True
         sage: sage.rings.infinity.is_Infinite(-oo)
         True
@@ -988,6 +992,9 @@ def is_Infinite(x) -> bool:
         sage: sage.rings.infinity.is_Infinite(ZZ)
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38022, "The function is_Infinite is deprecated; use 'isinstance(..., InfinityElement)' instead.")
+
     return isinstance(x, InfinityElement)
 
 
diff --git a/src/sage/rings/multi_power_series_ring_element.py b/src/sage/rings/multi_power_series_ring_element.py
index 32e16def317..70c882cc51c 100644
--- a/src/sage/rings/multi_power_series_ring_element.py
+++ b/src/sage/rings/multi_power_series_ring_element.py
@@ -157,7 +157,7 @@
 from sage.structure.richcmp import richcmp
 
 from sage.rings.finite_rings.integer_mod_ring import Zmod
-from sage.rings.infinity import infinity, is_Infinite
+from sage.rings.infinity import infinity, InfinityElement
 from sage.rings.integer import Integer
 from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
 from sage.rings.power_series_ring import is_PowerSeriesRing
@@ -1956,7 +1956,7 @@ def exp(self, prec=infinity):
         assert (val >= 1)
 
         prec = min(prec, self.prec())
-        if is_Infinite(prec):
+        if isinstance(prec, InfinityElement):
             prec = R.default_prec()
         n_inv_factorial = R.base_ring().one()
         x_pow_n = Rbg.one()
@@ -2053,7 +2053,7 @@ def log(self, prec=infinity):
         assert (val >= 1)
 
         prec = min(prec, self.prec())
-        if is_Infinite(prec):
+        if isinstance(prec, InfinityElement):
             prec = R.default_prec()
         x_pow_n = Rbg.one()
         log_x = Rbg.zero().add_bigoh(prec)
diff --git a/src/sage/rings/power_series_ring_element.pyx b/src/sage/rings/power_series_ring_element.pyx
index 8e1b76a7cc9..22a5cc46645 100644
--- a/src/sage/rings/power_series_ring_element.pyx
+++ b/src/sage/rings/power_series_ring_element.pyx
@@ -96,7 +96,7 @@ With power series the behavior is the same.
 # ****************************************************************************
 
 from cpython.object cimport Py_EQ, Py_NE
-from sage.rings.infinity import infinity, is_Infinite
+from sage.rings.infinity import infinity, InfinityElement
 
 from sage.rings.rational_field import QQ
 
@@ -1901,7 +1901,7 @@ cdef class PowerSeries(AlgebraElement):
         assert(val >= 1)
 
         prec = min(prec, self.prec())
-        if is_Infinite(prec):
+        if isinstance(prec, InfinityElement):
             prec = R.default_prec()
         n_inv_factorial = R.base_ring().one()
         x_pow_n = R.one()
@@ -1987,7 +1987,7 @@ cdef class PowerSeries(AlgebraElement):
         x = self
 
         prec = min(prec, self.prec())
-        if is_Infinite(prec):
+        if isinstance(prec, InfinityElement):
             prec = R.default_prec()
         n_inv_factorial = R.base_ring().one()
         x_pow_n = x
@@ -2140,7 +2140,7 @@ cdef class PowerSeries(AlgebraElement):
         x = self
 
         prec = min(prec, self.prec())
-        if is_Infinite(prec):
+        if isinstance(prec, InfinityElement):
             prec = R.default_prec()
         n_inv_factorial = R.base_ring().one()
         x_pow_n = x
@@ -2228,7 +2228,7 @@ cdef class PowerSeries(AlgebraElement):
         assert(val >= 1)
 
         prec = min(prec, self.prec())
-        if is_Infinite(prec):
+        if isinstance(prec, InfinityElement):
             prec = R.default_prec()
         n_inv_factorial = R.base_ring().one()
         x_pow_n = R.one()