In Java, every function must be wrapped by a class, but in Ruby, we can define a function without classes. Therefore, some years ago I used to suppose that:

There are no functions in Java, only methods. But for Ruby, we can have a function that isn't a method.

However, these days I have realized that: "Every function in Ruby is also a method".

But why can we define the function at the top-level scope, without creating classes for them, like Java? Or which class does this function belong to?

For example, I have the function increment

def increment(num)
  num + 1
end

We try to call increment this way:

self.increment 10
# or
self.send(:increment, 10)

Since self keyword contains a reference to the current object, the receiver for the current method, increment must be a method. Now let's check which object self reference to.

puts self
# => main
puts self.class
# => Object

You can see puts self code returns string "main", and it is an instance of Object, the root class of Ruby’s class hierarchy. So we can conclude that increment is an instance method in the Object class.
Technically speaking, Ruby automatically creates a main object as the top self object, it is the default receiver for top-level methods. Actually, all Ruby functions are private methods of Object.

p Object.private_instance_methods
# [:increment, :DelegateClass, :sprintf, ...]

Conclusion

• Every function in Ruby is also a method. It's an instance method of Object class.
• Ruby main object allows you to write simple functions and, at the same time, ensure sophisticated OO design.