In colloquial English this could trivially be understood as the distinction between defined and undefined terms.In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a variable may be said to be either free or bound. A free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not a parameter of this or any container expression. Some older books use the terms real variable and apparent variable for free variable and bound variable, respectively. The idea is related to a placeholder (a symbol that will later be replaced by some value), or a wildcard character that stands for an unspecified symbol.
The symbol "x" is said to be unbound by default, until another symbol; or an expression is bound to it. It represents a free variable.
Unless, and until bound to something free variables represent an unbounded entity. Something without limits, lacking value or quantification.
But that is exactly what the symbol "∞" represents!
If two symbols represent the same concept (an unbound quantity; or value) it follows by the identity axiom that the two symbols are synonymous and interchangeable.
X is identical to ∞ (x ≡ ∞)
∞ to Mathematicians, is like Truth to Philosophers; or like God to theists.
It means whatever you want it to mean.
“When I use a word,’ Humpty Dumpty said in rather a scornful tone, ‘it means just what I choose it to mean — neither more nor less.’
’The question is,’ said Alice, ‘whether you can make words mean so many different things.’
’The question is,’ said Humpty Dumpty, ‘which is to be master — that’s all.”