I hear it used quite often - "an almost infinite number of…” Surely it is complete nonsense. Infinity is a limitless concept. ‘Almost’ is a term that requires a limit.
I already know the answer, but I may as well ask for the sake of interest - Is it possible for there to be an “almost infinite” quantity of something?
I agree. People should use the more accurate term, “shitload”, to denote exceptionally large quantities.
But there are cases where a number is so large that for all real purposes it can be approximated by infinity. Maybe practically infinite might be better than almost infinite, though in such cases.
Bippy is right. The phrase “near infinite” is used as a synonym for “approximately infinite” in shitloads of cases.
Not as bad as “very unique.”
But surely, infinity is at least a million times larger than that number (at most - an infinity larger), therefore it is not ‘almost infinite’ or ‘practically infinite’.
Any number defined as ‘almost infinite’ is, without question, infinitely smaller than the infinite number. so it is pretty far from ‘almost’ infinite.
Just consider it a figure of speech. Sure, it doesn’t make sense when taken literally, but the same can be said about lots of figures of speech.
2[sup]80[/sup] is infinite for all practical purposes.
I agree that there are numbers which can really not be distinguished from infinity in all practical uses. For example:
(the number of cubic Planck lengths in the known universe)^googolplex
This far surpasses the number of anything countable in the universe, so it really is infinity for all intents and purposes.
Or a whole shitload, for very large values of shitload.
You know what I don’t get? “Unremarkable.” It just seems paradoxical. “That object or situation is so unmeriting of remark that it’s whole lack of remarkableness merits remark.”
Depends on what you mean by “practical”. If I weren’t so very lazy, I could probably dig up a problem in thermal physics where you get an intermediate figure of 2[sup]80[/sup] configurations in an ensemble or something like that.
Some Engineers are are also reputed to consider functions like iterated log to be 0 for any practical x. They are the equivalent of “almost zeroes.” (Didn’t Michael Richards star in that?)
I have been doing some work with strange numbers fields lately, one of which admits the existence of “integers” greater than any standard integer but less than infinity. To most people that makes them infinite, but they’re not. They are “almost infinite.”
It really is just a figure of speech.
OK, I checked my old thermal physics textbook and found in the first few pages the quantity (10[sup]20[/sup])! That’s way bigger than 2[sup]80[/sup].
Wait, is this a metric shitload, or an imperial shitload we’re talking about?
I suppose in very obscure circumstances, the phrase ‘almost infinite’ could make sense, but not in the circumstances it is generally used.
Consider this hypothetical situation. You’re walking along the X-axis of the curve y=1/x. You started out at x=20, and you’re walking towards x=0. As you get closer to x=0, you could reasonably say that ‘y is almost infinite’.
Actually, y would almost be undefined. Back to the drawing board as far as examples are concerned… however, the idea remains that if you mean ‘almost’ in the sense of ‘soon to be’, then maybe the expression could occasionally make sense.
Usually ‘practically infinite’ is more reasonable, though.
~ Isaac
PS Actually, now that I reread the original post, the expression you’re after is ‘an almost infinite number of things’. So I guess I’ve been pretty much foiled. Ah well, I’ll leave it there, since I thought it was a good crack at justifying such a blatantly ridiculous expression.
2^80 = 1208925819614629174706176
10^20 = 100000000000000000000
I think.
2[sup]80[/sup] is approximately equal to 10[sup]24[/sup].
In general, 2[sup]10x[/sup] is approximately equal to 10[sup]3x[/sup].
Are you working in the hyperreals, or something more exotic?
Nope. .999… is almost infinitely close to 1, but it’s .000…1 (which is almost infinitely small, .000…01 would be infinitely small)
Just kidding 
He said 10^20 factorial, which truly would be a huge giant shitload.