Fix printing of InexactError for Inf16 arg and similar (#52491)

Resolves #51087
Closes #51163

Use `show` as pointed out in
#51163 (comment).

base/errorshow.jl

@@ -181,7 +181,13 @@ function showerror(io::IO, ex::InexactError)
     print(io, "InexactError: ", ex.func, '(')
     T = first(ex.args)
     nameof(T) === ex.func || print(io, T, ", ")
-    join(io, ex.args[2:end], ", ")
+    # `join` calls `string` on its arguments, which shadows the size of e.g. Inf16
+    # as `string(Inf16) == "Inf"` instead of "Inf16". Thus we cannot use `join` here.
+    for arg in ex.args[2:end-1]
+        show(io, arg)
+        print(io, ", ")
+    end
+    show(io, ex.args[end])
     print(io, ")")
     Experimental.show_error_hints(io, ex)
 end

test/errorshow.jl

@@ -1090,3 +1090,17 @@ let e = @test_throws MethodError convert(TypeCompareError{Float64,1}, TypeCompar
     @test  occursin("TypeCompareError{Float64,1}", str)
     @test !occursin("TypeCompareError{Float64{},2}", str) # No {...} for types without params
 end
+
+@testset "InexactError for Inf16 should print '16' (#51087)" begin
+    @test sprint(showerror, InexactError(:UInt128, UInt128, Inf16)) == "InexactError: UInt128(Inf16)"
+
+    for IntType in [Int8, Int16, Int32, Int64, Int128, UInt8, UInt16, UInt32, UInt64, UInt128]
+        IntStr = string(IntType)
+        for InfVal in Any[Inf, Inf16, Inf32, Inf64]
+            InfStr = repr(InfVal)
+            e = @test_throws InexactError IntType(InfVal)
+            str = sprint(Base.showerror, e.value)
+            @test occursin("InexactError: $IntStr($InfStr)", str)
+        end
+    end
+end