Methods of running a script on Linux distro

[Vysero]

Normally you would chmod +x script.py to make it executable without having to specify python on the command line explicitly.

I have the script.py on my desktop. I am in: ~/Desktop: directory and when I type: sudo chmod +x script.py. It gives the error:

Output:
rob@linux038:~/Desktop$ sudo chmod +x script.py
[sudo] password for rob: 
chmod: cannot access 'script.py': No such file or directory

So I tried:

rob@linux038:~/Desktop$ sudo chmod +x script
rob@linux038:~/Desktop$

So it worked?? I am not sure, lol how do I check if the link was created any idea?