The Wikipedia definiton of equality gives it as a 'relationship between two expressions'
This confuses me as when we define mathematical expressions like 2+2=4 it makes no sense to say that '=' or 'equals to' relates the two expressions as it would mean that '2+2' and '4' are representing themselves as expressions as opposed to denoting or naming the objects.
I think in mathematical contexts when we use expressions it is always to unambiguously name an object, for example: '2 is an element of N' is meaningless if '2' represents itself as an expression.
I understand there is a relation between the expressions whose value are the same but is defining this relationship as 'equality' and saying it is denoted by '=' correct? It seems that '=' should denote a relationship an object has with itself.
Take x where x is any real number,
2x=x+1 is true when x=1 but not for any other values, this is a constraint how are the two strings of symbols related by equality? Whether we can conclude that the two have the same value depending on the interpretation.
If we define '=' as a relation between objects we have no issue with this.