From the Isavasya, [circa 1,000 BCE] 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 what this formally ‘Undefined Concept’ is. ‘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.
The symbol ‘0’ has been around for a long time. But the symbol ‘∞’ for ‘Infinity’ however is relatively new, less than 500 years old. Its age overlaps with the period of rampant confusion that has characterized the use of this idea.
The grizzled Dharmic monks and the geezers around the fountain-square in old Athens didn’t like words like ‘All, Everything, Eternity, Infinity’ very much.
‘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 its bounds as the ‘Unbounded’.
Sort of like the name: ‘Nameless’.
The idea of ‘Infinity’ has long attracted the mathematically adventurous [we’ll get to it with Georg Cantor and ‘Set Theory’].
And the philosophically credulous. The favorite chant of the rising guru is: ‘Brahman is the All!’ And the threat of the Preacherman: ‘Thou shalt fry for all Eternity’ [Infinity on a Time-Axis].
‘Infinite Regress’? A term coined to suggest its user needs serious psychiatric help. Logician’s exit the room in its presence. The resolution of the Self-Eating Expression is ‘Infinite Regress’ in its most militant form: ‘All Words Lie!’ And that’s a Lie’. Ad Infinitum.
Have you ever had the compelling desire to fly faster than Light? Yes?
We’ll, you can’t do it. And why can’t you do it? The folks who worked out the Theory of Relativity found that as you approach the speed of Light, the amount of energy needed to move you [or for that matter, a single electron] ‘Tends to Infinity’.
While you snuggle into the empty space of a vacuum tube [‘Tends to Zero’], enthusiastic Scientists are vigorously seeking a ‘Theory of Everything’. Any such theory, by that very fact, invalidates itself.