The symbol ‘0’ has been around for a long time. But the symbol ‘∞’ for ‘Infinity’ however is relatively new, less than 500 years old, coincident with the birth of Science and its need for abstract measurements [the Universe is ‘Finite but Unbounded’?!].
You can explore a Self-Inclusive Expression such as ‘∞’ in counterpoint to a Self-Negating Expression but it is exceptionally difficult to effect. You will spin around forever in self-referential loops.
The grizzled Dharmic monks and the geezers around the fountain-square in old Athens didn’t like the word very much, rarely used it. [It parallels their reluctance to grant the ‘Principle of Induction’ the status of ‘Law’]. And why not?
‘Infinity’ is from the Latin In-finitas, for ‘Unbounded, Unbordered’. The bells should go off right there. To give definition is to mark a boundary. And here we begin by defining something as the ‘Unbounded’ [‘The Definition of Defintion’].
From the Isavasya, the briefest of the principal Upanishads: ‘When taken away from the Infinite Whole [Purnam], the Infinite Whole remains the Infinite Whole’.
Infinity minus ten trillion is still Infinity. That’s the definition for this formally ‘Undefined Concept’. ‘Infinity’ is that which doesn’t budge when you take something away from it. Or add something to it.
We don’t quite know what Infinity is. But we are quite sure that ‘Infinity plus one’ is the same as it. The functional definition of this idea has remained pretty much the same since antiquity.
[As part of the light-headedness surrounding the Symbol ‘∞’, it is common to see it conflated with the Greek ‘Oroborous’, a graphic symbol for the Self-Negating Expression itself. See: ‘The Scope Of The SEE’.]