The idea of ‘Infinity’ has long attracted the mathematically adventurous. And the philosophically credulous.
The symbol ‘0’ has been around for a long time. But the symbol ‘∞’ for ‘Infinity’ however is relatively new, making its appearance with the birth of Science and its need for abstract measurements [the Universe is ‘Finite but Unbounded’?].
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’; see the Post]. 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‘.
From the Isavasya Upanishad: ‘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.
‘Infinite Regress’? A term coined to suggest its user needs serious psychiatric help. The resolution of the Self-Eating Expression is ‘Infinite Regress’ in its most militant form.
The always effective threat of the Preacherman that brings the obdurate to their knees: ‘Thou shalt fry for all Eternity’ [Infinity on a Time-Axis].
Have you ever had the compelling desire to fly faster than Light? 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 an inch [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. The folks don’t understand Self-Reference.
Wilhelm Leibniz along with Isaac Newton is credited with founding the Calculus. Lots of ‘Tending to Zero’ and ‘Tending to Infinity’ in it. He was alert to the Loop but avoided any direct confrontation with it [See Posts]. Explain that to the modern Mathematician.