"Progress.  But '~0' isn't a thing in this language, 'not' takes in propositions, which have the values of truth or falsehood, and spits out falsehood or truth.  'Not four' isn't a number - or if you wanted it to talk about all the numbers except four, we'd have to start introducing collections and that's a big ol' subject.  ~= isn't already symbol in our language either, and in fact you don't particularly need to define a new symbol for it.  Next rewrite?" 

"Progress.  But '~0' isn't a thing in this language, 'not' takes in propositions, which have the values of truth or falsehood, and spits out falsehood or truth.  'Not four' isn't a number - or if you wanted it to talk about all the numbers except four, we'd have to start introducing collections and that's a big ol' subject.  ~= isn't already a symbol in our language either, and in fact you don't particularly need to define a new symbol for it.  Next rewrite?" 

"Progress.  But '~0' isn't a thing in this language, 'not' takes in propositions, which have the values of truth or falsehood, and spits out falsehood or truth.  'Not four' isn't a number - or if you wanted it to talk about the collection of all numbers except four, we'd have to start introducing collections and that's a big ol' subject.  ~= isn't already a symbol in our language either, and in fact you don't particularly need to define a new symbol for it.  Next rewrite?"