jq, 20 bytes
[range(max)+1]==sort
Explanation
max # Get the maximum of the input
range( ) # Generate the non-negative integers below that
+1 # Add 1 to each of them
[ ] # Collect as list
sort # Sort the input list
== # Compare the two lists
jq, 20 bytes
[range(max)+1]==sort
Explanation
max # Get the maximum of the input
range( ) # Generate the non-negative integers below that
+1 # Add 1 to each of them
[ ] # Collect as list
sort # Sort the input list
== # Compare the two lists