Question

State that 'the limit of f(x) as x approaches zero' is a slight use-mention distinction example as we use x as a possible denotation of a number, and then later as a 'variable' a symbol which approaches a particular value. Are we using 'x' differently (one as an unassigned object) the other as a symbol which may take assignments (the behaviour under these assignments being the object of study).

Answer 1

In mathematics, the use of x as a limit and as a variable is a slight use-mention distinction. The distinction arises because x can represent a number and also a symbol that approaches a particular value.

Step-by-step explanation:

The subject of your question is mathematics. In mathematics, x can be used in different ways. When we say 'the limit of f(x) as x approaches zero', we are using x as a possible denotation of a number. However, later when we refer to x as a 'variable', we are using it as a symbol which approaches a particular value.

So, in one case, x is an unassigned object representing a number, and in the other case, x is a symbol that may take assignments and its behavior under these assignments is the object of study.