This isn't about the shell of a calculator though, but the functionality. Like if the only operations are addition and subtraction, theoretically you could derive the effects of other operations but it's extremely limiting.
So yeah, half of Python might still be Turing-complete, but it wouldn’t really be Python for any practical purpose.
Just like how a device that can’t multiply or divide is not a 4-function calculator; it’s more like an adding machine. Many of which did multiply by serial addition.
If you write a program in python, say a hello world:
'
def hello_world():
print("hello, world")
'
Is that not python? Yet it uses a subset of python?
That program can be run by either a python runtime, or a python subset runtime.
Now if you were to run a python subset program, like a hello world, you would get:
'
def hello_world():
print("hello, world")
'
Whoah, it's the same thing.
Turns out every program you write with a subset of a language, is valid for the super language.
Subjectively also, if the subset is big enough, it feels like that language, if it uses 'def' for functions, that's python. 'I know it when I see it' kinda deal.
I think the confusion comes from the mathematical folk reading "subset of X is X", and implying that "subset of X=X". But this is natural language, not mathematical language, when I say that "dog is mammal", I'm not saying that "dog = mammal" I'm saying that "dog ∈ mammal", and "subset of python ∈ python"