I'm relatively new here myself but I've unleashed a torrent I'd forgotten I have.

How big is "infinite" and how small "infinitesimal"? That is exactly like asking how big and how small is "finite"? Thank you, I've never once in my life until this moment of coming across your thread thought to ask myself or anyone just how big can finite ever get, and in turn just how small can it get?

Infinitesimal means 'infinitely small' as opposed to infinite. Infinitely ... small. "Infinite", now it can [qualify] either as a lot or a little of whatever. Phrase: "It has an infinite quality to it." What does it mean? Does it mean its bluer than blue, or redder than red? Does it mean its hotter than hot, or colder than cold? Does it mean '+1', as in someone telling you the number is 10 and you come back with +1. They go, "then the number is 11." and you come back with "+1" (to infinity). How rich is richer than rich? Infinitely rich. How poor is poorer than poor? Infinitely poor, aka infinitesimally rich.

So now, what, or how, is infinite bigness / infinite smallness (aka infinitesimal) to be qualified? The answer is bigger (infinite) than big (finite), and smaller (infinite / infinitesimal) than small (finite). Comparatively speaking though, infinite as opposed to infinitesimal is something different all together because, therein, there is no finiteness, as we define it, whatsoever to that question and comparison. Wrap your head around this: Having left out finite, however infinite you go (up, up, up, and out) in anything, a number or quality, the only down and in from there is infinitesimal. And on the other side, however infinitesimal you go (down, down, down, and in) the only up and out from there is infinite.

Two infinites can cancel to finite. Two infinitesimals can cancel to finite. Infinite and infinitesimal do not cancel to finite. They turn in to one another, they wrap in to one another, to 'infinite' (or to 'infinity', however you want to put it),

The more interesting question is how much greater, bigger or smaller, either up and out, or down and in, than any particular finite can finite go? That question develops a boundarylessness to the particular finite. A "boundaryless finite" is still finite, but with a heck of a 'potential' for infinite.

Chaos Theory goes into the problem with grainy detail (finite) versus overall smoothness (infinity). Grainy detail layer (finite), and up and out to an overall layer of smoothness (infinite). But if you think it ends there, you've got another think coming. Up, up, and out of [that] layer of smoothness, according to Chaos Theory, you discover you've realized yet another layer of grainy detailing (of finite over infinite!). Up, up, and out, of that layer of grainy detailing, only to discover yet another layer of infinity's smoothness. And on and on to 'infinity' (monotonously). If you then get the feeling you're spinning your wheels, you're exactly right. No matter the hyper-spatiality of the layering, the reduction is to two, layer(s) of finite grainy detail, and layer(s) of infinitely smooth. And you discover that the two are an exact match...that they are exact equals (Finite ||| Infinite / infinitesimal... Finite mass ||| Infinite mass (Big Crunch) / infinitesimal mass (Big Hole / Vacuum / Space).... Finite universe(s) ||| Infinite Universe / Infinitesimal Universe.... The two are an exact match... they are exact equals (because [infinite / infinitesimal] turns to itself; circles to itself; wraps into itself.... But still is infinite / still is infinitesimal, always)).

And by the way, "turns to itself"; [turn to], [to turn], is literally 'en trope'; gk 'tropos' (turn); en-tropy; entropy: The turn or wrap of infinite / infinitesimal to/into itself (infinite to/into infinitesimal) (infinitesimal to/into infinite). Now why didn't I include the Big Bang, and the energy of the Big Bang, in [my (!)] explanation of infinite / infinitesimal above? I included the Big Crunch and its mass...? Because the Big Bang and its energy do not belong to Chaos Theory's layer(s) of 'infinite smoothness'. they belong to its layer(s) of 'finite grainy detail'. A matter of 'Time' rather than 'Space'. A matter of 'Energy' rather than 'Mass'. A matter of [time-energy] rather than [space-time] and/or [mass-energy] ... and/or [mass-space]. The biggest, and/or smallest 'Mirror' vacuum energy of them all. Facing in the Mirror (Big Gravity's Big bent Mirror), a double ended (Bookended) Beginning to Time; facing to >|0|< (facing in to '0'-point (Now) (the End of Time, as Stephen Hawking once put it, though not quite as I put it here)). For a 'finite' (rather than an 'infinite'), you can't get more 'hyper-finite' than that.