# Anti-Infinity **URL:** \ **Category:** Great Debates\ **Created:** [January 8, 2000, 7:29pm UTC](https://boards.straightdope.com/t/anti-infinity/17424 "2000-01-08T19:29:00Z")\ **Posts on this page:** 20\ **Page:** 3
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [January 10, 2000, 6:29am UTC](https://boards.straightdope.com/t/anti-infinity/17424/41 "2000-01-10T06:29:00Z")
Beeruser: > [@](#): > > Do I get a consolation prize, or something? Yes, you get the consolation of RTFirefly’s penumbric persiflage. slythe: > [@](#): > > I just tossed the whole equation out the window when you tried to divide by zero, and came up with a definition of Infinity, which cannot be proven or disproven with the faulty equations you provided. I never “tried to divide by zero”. PeeQueue: > [@](#): > > And besides, why would you want to do away with the concept of infinity after all the great new things it has enabled mathematics to do? Like what? Anti-infinity allows you to do meaningful multiplication of repeating decimals. For example: 4(.7[n]) 4(.7) = 2.8 4(.77) = 3.08 4(.777) = 3.108 4(.7777) = 3.1108 4(.77777) = 3.11108 . . . 4(.7[n]) = 3.1[n-2]08 The quaint infinity concept forces you to give the answer as 3.11111…, discarding now not just one, but _two whole significant places_. Tris: > [@](#): > > An infinite number of zeros, followed by a one? Please. You can’t be serious, can you? Good arithmetic makes sense when you say it out loud. I’m not the one saying things like “infinite number”. You need to take your argument to the infinitists. RTFirefly: > [@](#): > > Infinity isn’t a number; it’s the concept of continuation without end. [knocking on your forehead…] Hello? Anybody there? For your homework, find how many times I said that infinity isn’t a number, and then divide that by how many times I said that infinity is a number. Define your operation. > [@](#): > > Oh yeah. I could prove that there’s nothing in between .999… and 1, but that’s an epsilon proof. (As in, “let epsilon \> 0…”, that phrase that has intimidated generations of calculus students.) You don’t want to mess with epsilons. No, what I don’t want to mess with are condescending arrogrant fops who think calculus is hard — not that you _are_ one, of course. I’m not unfamiliar with Cantor’s derivation of infinity from endpoints of line segments. I simply say that it’s a bunch of hooey. Infinity is an unnecessary entity. That makes it one too many entities. * * * “It is lucky for rulers that men do not think.” — Adolf Hitler ---
**Author:** ![Dark\_Wing\_Duck](https://avatars.discourse-cdn.com/v4/letter/d/f0a364/32.png) [@Dark\_Wing\_Duck](https://boards.straightdope.com/u/Dark_Wing_Duck)\ **Post date:** [January 9, 2000, 7:37pm UTC](https://boards.straightdope.com/t/anti-infinity/17424/42 "2000-01-09T19:37:00Z")
Lib, what exactly is infinity? Seems like knowing that would help to decide whether it exists or not. ---
**Author:** ![Phaedrus](https://avatars.discourse-cdn.com/v4/letter/p/53a042/32.png) [@Phaedrus](https://boards.straightdope.com/u/Phaedrus)\ **Post date:** [January 9, 2000, 8:36pm UTC](https://boards.straightdope.com/t/anti-infinity/17424/43 "2000-01-09T20:36:00Z")
Beeruser: Hey, aren’t you the guy they said couldn’t use logic??!?!?!?!! This is way over my head but I think it proves a long held point of mine. THE PEOPLE WHO POST HERE ARE BRILLIANT!!! Ken ---
**Author:** ![RTFirefly](https://avatars.discourse-cdn.com/v4/letter/r/c77e96/32.png) [@RTFirefly](https://boards.straightdope.com/u/RTFirefly)\ **Post date:** [January 9, 2000, 10:08pm UTC](https://boards.straightdope.com/t/anti-infinity/17424/44 "2000-01-09T22:08:00Z")
Me: Infinity isn’t a number; it’s the concept of continuation without end. > [@](#): > > [knocking on your forehead…] > > Hello? Anybody there? And your problem is? Biff in _Back to the Future_ didn’t have a brain either, Lib. I’m doing mathematics; you’re doing finite arithmetic and bad sophistry. Quit puddling up the carpet. ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [January 9, 2000, 10:09pm UTC](https://boards.straightdope.com/t/anti-infinity/17424/45 "2000-01-09T22:09:00Z")
Dark Wing Duck: > [@](#): > > Lib, what exactly is infinity? Pick a math book, any math book. You’ll see all kinds of attempts at defining it, including RT’s “the concept of continuation without end”. It is also said to be the slope of a vertical line, a nonterminating series, or even the solution set of N / 0. All those are bogus. It is a remarkably mystical concept. It is amazing to me that an atheist could buy into it at all. * * * “It is lucky for rulers that men do not think.” — Adolf Hitler ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [January 9, 2000, 10:20pm UTC](https://boards.straightdope.com/t/anti-infinity/17424/46 "2000-01-09T22:20:00Z")
RTFirefly: > [@](#): > > And your problem is? My problem is your intellectual snobbery. If you think we can carry on a serious conversation when you chuck up stuff like — “glad I didn’t throw away my logic texts when I quit being a math professor,” or “I’ve corrected a lot of math homework in my life, but this is the first time I’ve done it over the Internet!,” or “You don’t want to mess with epsilons,” or “to see what (if anything) you’ve shown,” — things adults don’t usually say to other adults whom they respect, then you’re delusional. I have no intention of having a pissing contest with you, which is something you seem to troll around wherever I post trying to stir up. If you have nothing substantive to contribute, why don’t you just back the fuck off? Otherwise, make rational arguments and quit acting like a snotty brat. * * * “It is lucky for rulers that men do not think.” — Adolf Hitler ---
**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\ **Post date:** [January 9, 2000, 10:54pm UTC](https://boards.straightdope.com/t/anti-infinity/17424/47 "2000-01-09T22:54:00Z")
Here’s a non-bogus definition of infinity: A set is infinite if it can be put into a 1-1 correspondence with a proper subset of itself. An infinite number would be the number of elements of an infinite set. (Yes, I consider infinity to be a number–not a real number, but a transfinite number, and you can do arithmetic with transfinite numbers). ---
**Author:** ![Surgoshan](https://avatars.discourse-cdn.com/v4/letter/s/e95f7d/32.png) [@Surgoshan](https://boards.straightdope.com/u/Surgoshan)\ **Post date:** [January 9, 2000, 11:01pm UTC](https://boards.straightdope.com/t/anti-infinity/17424/48 "2000-01-09T23:01:00Z")
Lib, your second proof is true, but only insofar as n is a finite number. As n approaches infinity (the bigger it gets) the closer .9[n] gets to one, the closer 1 - .9[n] gets to 0. When n = infinity, 1-.9[n] = 0, .9[n] = 1. So the proofs aren’t really contradictory. ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [January 9, 2000, 11:04pm UTC](https://boards.straightdope.com/t/anti-infinity/17424/49 "2000-01-09T23:04:00Z")
Cabbage: Are you, as an infinitist, saying that there is a 1-1 correspondence between the set of real numbers and the set of integers? If so, it contradicts RTFirefly’s assertion that “the set of real numbers … [is] too big to be put into [a] 1-1 correspondence with smaller infinite sets such as the integers or the rationals”. * * * “It is lucky for rulers that men do not think.” — Adolf Hitler ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [January 9, 2000, 11:07pm UTC](https://boards.straightdope.com/t/anti-infinity/17424/50 "2000-01-09T23:07:00Z")
Surgoshan: How can there be an “infinity”, other than as a meaningless conception, like a lawn sprite or a fairy? * * * “It is lucky for rulers that men do not think.” — Adolf Hitler ---
**Author:** ![Dark\_Wing\_Duck](https://avatars.discourse-cdn.com/v4/letter/d/f0a364/32.png) [@Dark\_Wing\_Duck](https://boards.straightdope.com/u/Dark_Wing_Duck)\ **Post date:** [January 9, 2000, 11:11pm UTC](https://boards.straightdope.com/t/anti-infinity/17424/51 "2000-01-09T23:11:00Z")
Ok, so there are all kinds of attempts at defining it, it is said to be this or that, but what is YOUR definition? Because unless we can agree on terms, this whole discussion boils down to, “There’s this thing, I can’t explain what it is, but it doesn’t exist. Prove me wrong.” ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [January 9, 2000, 11:27pm UTC](https://boards.straightdope.com/t/anti-infinity/17424/52 "2000-01-09T23:27:00Z")
Dark Wing Duck: Okay, fair enough. What I think doesn’t exist is a cardinality, A, for any field, F, where A + 1 = A. I find the concept about as useful as tits on a bull hog. Infinitists: What is 4 times .7…? * * * “It is lucky for rulers that men do not think.” — Adolf Hitler ---
**Author:** ![Dark\_Wing\_Duck](https://avatars.discourse-cdn.com/v4/letter/d/f0a364/32.png) [@Dark\_Wing\_Duck](https://boards.straightdope.com/u/Dark_Wing_Duck)\ **Post date:** [January 9, 2000, 11:28pm UTC](https://boards.straightdope.com/t/anti-infinity/17424/53 "2000-01-09T23:28:00Z")
Ok, so there are all kinds of attempts at defining it, it is said to be this or that, but what is YOUR definition? Because unless we can agree on terms, this whole discussion boils down to, “There’s this thing, I can’t explain what it is, but it doesn’t exist. Prove me wrong.” BTW, Cabbage didn’t say that an infinite set could be put into 1-1 correspondence with every proper subset of itself, just that there had to exist at least one proper subset with that property. And I have to admit, I’m curious as to why you picked the integers or the rationals as the subset to use as a contradictory example? Why not just the set {1}? ---
**Author:** ![Dark\_Wing\_Duck](https://avatars.discourse-cdn.com/v4/letter/d/f0a364/32.png) [@Dark\_Wing\_Duck](https://boards.straightdope.com/u/Dark_Wing_Duck)\ **Post date:** [January 9, 2000, 11:30pm UTC](https://boards.straightdope.com/t/anti-infinity/17424/54 "2000-01-09T23:30:00Z")
Sorry, didn’t mean to double-post that first paragraph. ---
**Author:** ![Spiritus\_Mundi](https://avatars.discourse-cdn.com/v4/letter/s/c68b51/32.png) [@Spiritus\_Mundi](https://boards.straightdope.com/u/Spiritus_Mundi)\ **Post date:** [January 9, 2000, 11:31pm UTC](https://boards.straightdope.com/t/anti-infinity/17424/55 "2000-01-09T23:31:00Z")
Libertarian: You are being either disengenuous or sloppy. You are also ignoring the question of your own notations. > [@](#): > > Hypothesis: .9… equals (or does not equal) 1. I have pointed out more than once that the notation .9… is accepted in mathematics to mean an unending repetition of digits. You, in the hope of disproving a well established field of mathematics, are using notation that implies that very field. If you do not mean .9… to be an infinite repetition, then you specify that you are using notation in a non-standard way. In that case, of course, proof 1 is trivially incorrect. Proof 2 is trivially correct but infinitely uninteresting. You have managed to prove that a particular fraction does not equal 1. It implies nothing about the concept of infinity, of course, since you have simply solved a finite equation. * * * - The best lack all conviction The worst are full of passionate intensity. \* ---
**Author:** ![Spiritus\_Mundi](https://avatars.discourse-cdn.com/v4/letter/s/c68b51/32.png) [@Spiritus\_Mundi](https://boards.straightdope.com/u/Spiritus_Mundi)\ **Post date:** [January 9, 2000, 11:37pm UTC](https://boards.straightdope.com/t/anti-infinity/17424/56 "2000-01-09T23:37:00Z")
Afraid I just can’t let this one slide: > [@](#): > > I’m not unfamiliar with Cantor’s derivation of infinity from endpoints of line segments. I simply say that it’s a bunch of hooey. Cantor’s work is, quite literally, brilliant. It is also quite a bit more rigorous than what you have provided here. > [@](#): > > [infinity] is a remarkably mystical concept. It is amazing to me that an atheist could buy into it at all. Mathematical infinities (there are just a few more that one) are not at all mystical in nature. Mystics often usurp the concept of mathematical infinity to “explain” their faiths. They usually get it wrong. That says nothing about the math, only the mystics. * * * - The best lack all conviction The worst are full of passionate intensity. \* ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [January 9, 2000, 11:39pm UTC](https://boards.straightdope.com/t/anti-infinity/17424/57 "2000-01-09T23:39:00Z")
Spiritus: Of _course_ I don’t mean .9… to be an “infinite” expression, whatever that is. And what is uninteresting about the implication that there is a smallest (and largest) non-zero real number? And what is 4 times .7…? And why is everybody so dour? Didn’t someone complain that there were too many religious and political threads? So, I gave everybody one that is religion-politics free. * * * “It is lucky for rulers that men do not think.” — Adolf Hitler ---
**Author:** ![Dark\_Wing\_Duck](https://avatars.discourse-cdn.com/v4/letter/d/f0a364/32.png) [@Dark\_Wing\_Duck](https://boards.straightdope.com/u/Dark_Wing_Duck)\ **Post date:** [January 10, 2000, 12:04am UTC](https://boards.straightdope.com/t/anti-infinity/17424/58 "2000-01-10T00:04:00Z")
Lib, in an earlier post, you gave the largest and smallest positive real numbers as ABS((0.0[n-1]1)) and ABS((1 / (0.0[n-1]1))). Might I ask the value of n in those expressions? ---
**Author:** ![Dark\_Wing\_Duck](https://avatars.discourse-cdn.com/v4/letter/d/f0a364/32.png) [@Dark\_Wing\_Duck](https://boards.straightdope.com/u/Dark_Wing_Duck)\ **Post date:** [January 10, 2000, 12:13am UTC](https://boards.straightdope.com/t/anti-infinity/17424/59 "2000-01-10T00:13:00Z")
Because whatever n is, ABS(0.0[n]1) is less than ABS((0.0[n-1]1)). Hey, I just discovered the smallest positive number! ---
**Author:** ![Dark\_Wing\_Duck](https://avatars.discourse-cdn.com/v4/letter/d/f0a364/32.png) [@Dark\_Wing\_Duck](https://boards.straightdope.com/u/Dark_Wing_Duck)\ **Post date:** [January 10, 2000, 12:15am UTC](https://boards.straightdope.com/t/anti-infinity/17424/60 "2000-01-10T00:15:00Z")
Found another one, ABS(0.0[n+1]1). [Previous page](https://boards.straightdope.com/t/anti-infinity/17424.md?page=2) [Next page](https://boards.straightdope.com/t/anti-infinity/17424.md?page=4)