# Knowledge without Proof **URL:** \ **Category:** Great Debates\ **Created:** [October 13, 2005, 8:15am UTC](https://boards.straightdope.com/t/knowledge-without-proof/326040 "2005-10-13T08:15:46Z")\ **Posts on this page:** 20\ **Page:** 6
**Author:** ![bitwise](https://avatars.discourse-cdn.com/v4/letter/b/ea5d25/32.png) [@bitwise](https://boards.straightdope.com/u/bitwise)\ **Post date:** [October 19, 2005, 3:42am UTC](https://boards.straightdope.com/t/knowledge-without-proof/326040/101 "2005-10-19T03:42:40Z")
> [@ultrafilter](#): > > This is the error in your argument. ∞ on its own is a meaningless symbol, and in any context where it does have meaning, it doesn’t represent a single value. Are you deliberately excluding the extended reals from consideration? ---
**Author:** ![andros](https://avatars.discourse-cdn.com/v4/letter/a/e480ec/32.png) [@andros](https://boards.straightdope.com/u/andros)\ **Post date:** [October 19, 2005, 3:49am UTC](https://boards.straightdope.com/t/knowledge-without-proof/326040/102 "2005-10-19T03:49:35Z")
> [@bitwise](#): > > This is not quite correct; automated theorem proving is a field of study. It is also possible to represent 1/3 with perfect accuracy on a computer. It really depends on your representation. I can represent 1/3 as a pair of integers; I could also use some kind of base-3 representation. More accurately, then, no computer can manipulate .3333333… _in that form_, as it’s nonterminating. It doesn’t _have_ to, of course. That’s the great thing about math. And computers. And **Kozmic** , what the hell is your point of debate here? Seriously, are you just having us on? ---
**Author:** ![Kozmik](https://avatars.discourse-cdn.com/v4/letter/k/8dc957/32.png) [@Kozmik](https://boards.straightdope.com/u/Kozmik)\ **Post date:** [October 19, 2005, 11:35am UTC](https://boards.straightdope.com/t/knowledge-without-proof/326040/103 "2005-10-19T11:35:43Z")
> [@Kozmik](#): > > 3 + 3 = 2 + 4 > > π + π = Here are the counterexamples. 3 - 3 = 0 π - π = 0 ---
**Author:** ![Kozmik](https://avatars.discourse-cdn.com/v4/letter/k/8dc957/32.png) [@Kozmik](https://boards.straightdope.com/u/Kozmik)\ **Post date:** [October 19, 2005, 11:49am UTC](https://boards.straightdope.com/t/knowledge-without-proof/326040/104 "2005-10-19T11:49:47Z")
x + x = y + z 3 + 3 = 2 + 4 y and z cannot be 3 x + x = y + z π + π = \_\_\_ + \_\_\_ y and z cannot be π ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [October 19, 2005, 2:02pm UTC](https://boards.straightdope.com/t/knowledge-without-proof/326040/105 "2005-10-19T14:02:43Z")
> [@bitwise](#): > > Are you deliberately excluding the extended reals from consideration? At this point, it seems simplest to keep things in the standard reals. And even in the extended reals, ∞ is not a “number” in the same sense that the other elements are. **Kozmik** , do you actually have a point? Can you summarize it in plain English? ---
**Author:** ![Kozmik](https://avatars.discourse-cdn.com/v4/letter/k/8dc957/32.png) [@Kozmik](https://boards.straightdope.com/u/Kozmik)\ **Post date:** [October 19, 2005, 2:37pm UTC](https://boards.straightdope.com/t/knowledge-without-proof/326040/106 "2005-10-19T14:37:49Z")
x + x = y + z 3 + 3 = 2 + 4 y and z cannot be 3 x + x = y + z π + π = 6 + \_\_\_ z cannot be π π - π = 0 My point: The real numbers 3, 2, 4, 6, and 0 are precise. **The real number that solves π + π = 6 + \_\_\_ can never be precise.** ---
**Author:** ![andros](https://avatars.discourse-cdn.com/v4/letter/a/e480ec/32.png) [@andros](https://boards.straightdope.com/u/andros)\ **Post date:** [October 19, 2005, 2:42pm UTC](https://boards.straightdope.com/t/knowledge-without-proof/326040/107 "2005-10-19T14:42:42Z")
Horseshit, it’s can’t be. The missing term–the real number you’re seeking–is _n_, where _n_ = (2_π_-6). It is a real number. Why on earth does it shock you that an irrational number–2_π_–cannot be expressed as the sum of two integers? That’s just silly. ---
**Author:** ![SentientMeat](https://avatars.discourse-cdn.com/v4/letter/s/43a26b/32.png) [@SentientMeat](https://boards.straightdope.com/u/SentientMeat)\ **Post date:** [October 19, 2005, 2:46pm UTC](https://boards.straightdope.com/t/knowledge-without-proof/326040/108 "2005-10-19T14:46:13Z")
**Kozmik** , this thread is proof that you have no knowledge of maths. ---
**Author:** ![Voyager](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/voyager/32/133_2.png) [@Voyager](https://boards.straightdope.com/u/Voyager)\ **Post date:** [October 19, 2005, 4:44pm UTC](https://boards.straightdope.com/t/knowledge-without-proof/326040/109 "2005-10-19T16:44:17Z")
> [@bitwise](#): > > This is not quite correct; automated theorem proving is a field of study. It is also possible to represent 1/3 with perfect accuracy on a computer. It really depends on your representation. I can represent 1/3 as a pair of integers; I could also use some kind of base-3 representation. Base 3 will work for that number, but not others. And yes, I have heard of math packages operating on fractions. But even these will not be able to represent all numbers. You might even be able to represent e as a series - you’ll never terminate the calculation, but it might be possible to have a window of the fractional part you would have to represent. ---
**Author:** ![Voyager](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/voyager/32/133_2.png) [@Voyager](https://boards.straightdope.com/u/Voyager)\ **Post date:** [October 19, 2005, 4:52pm UTC](https://boards.straightdope.com/t/knowledge-without-proof/326040/110 "2005-10-19T16:52:51Z")
I am slow to anger, but I’ve had enough. All of you who have been so admirably restraining yourselves, join me [here.](http://boards.straightdope.com/sdmb/showthread.php?p=6701550#post6701550) ---
**Author:** ![Voyager](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/voyager/32/133_2.png) [@Voyager](https://boards.straightdope.com/u/Voyager)\ **Post date:** [October 19, 2005, 4:55pm UTC](https://boards.straightdope.com/t/knowledge-without-proof/326040/111 "2005-10-19T16:55:40Z")
> [@andros](#): > > Why on earth does it shock you that an irrational number–2_π_–cannot be expressed as the sum of two integers? That’s just silly. This has real life applications. Votes for officers of the MIT Science Fiction Society can be cast for as many candidates as you wish, but have to add up to 1. Negative numbers are not allowed, but irrational numbers are welcome. Typical vote tallies contain several fractions of e and pi and often even more obscure ones. ---
**Author:** ![astro](https://avatars.discourse-cdn.com/v4/letter/a/9dc877/32.png) [@astro](https://boards.straightdope.com/u/astro)\ **Post date:** [October 19, 2005, 5:50pm UTC](https://boards.straightdope.com/t/knowledge-without-proof/326040/112 "2005-10-19T17:50:37Z")
Kozmik, this is all leading up to the [time cube](http://www.timecube.com/) hypothesis isn’t it? ---
**Author:** ![alterego](https://avatars.discourse-cdn.com/v4/letter/a/6bbea6/32.png) [@alterego](https://boards.straightdope.com/u/alterego)\ **Post date:** [October 19, 2005, 5:56pm UTC](https://boards.straightdope.com/t/knowledge-without-proof/326040/113 "2005-10-19T17:56:22Z")
> [@andros](#): > > And hey, if you really want to see blown minds, check out the application of the Euler identity in which _x_=_π_: > > _e[sup]iπ[/sup]_ + 1 = 0 > Put _that_ in your pipe and smoke it. That one’s pretty good. It ruffles my feathers even more that 0[sup]0[/sup] = 1 ---
**Author:** ![andros](https://avatars.discourse-cdn.com/v4/letter/a/e480ec/32.png) [@andros](https://boards.straightdope.com/u/andros)\ **Post date:** [October 19, 2005, 6:02pm UTC](https://boards.straightdope.com/t/knowledge-without-proof/326040/114 "2005-10-19T18:02:04Z")
> [@astro](#): > > Kozmik, this is all leading up to the [time cube](http://www.timecube.com/) hypothesis isn’t it? :smack: ---
**Author:** ![Ogre](https://avatars.discourse-cdn.com/v4/letter/o/ecb155/32.png) [@Ogre](https://boards.straightdope.com/u/Ogre)\ **Post date:** [October 19, 2005, 7:12pm UTC](https://boards.straightdope.com/t/knowledge-without-proof/326040/115 "2005-10-19T19:12:27Z")
> [@andros](#): > > FWIW, yes I do think it’s true and luckily Ultrafilter did the complicated graduate-level work to solve that mathematical stumper. Hopefully a second thread devoted to why 1+1=2 will not be forthcoming. This cracked me up. 🙂 Can you believe I was actually relieved when he unveiled his “infinity hypothesis?” My first thought was, “Thank God he’s not talking about _phi_.” ---
**Author:** ![Ogre](https://avatars.discourse-cdn.com/v4/letter/o/ecb155/32.png) [@Ogre](https://boards.straightdope.com/u/Ogre)\ **Post date:** [October 19, 2005, 7:31pm UTC](https://boards.straightdope.com/t/knowledge-without-proof/326040/116 "2005-10-19T19:31:22Z")
> [@Ogre](#): > > This cracked me up. 🙂 > > Can you believe I was actually relieved when he unveiled his “infinity hypothesis?” My first thought was, “Thank God he’s not talking about _phi_.” …although phi is also an irrational, I just realized. oooooooooWEEEEEEEEEEEEEEoooooooooooooooo ---
**Author:** ![Cervaise](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cervaise/32/16693_2.png) [@Cervaise](https://boards.straightdope.com/u/Cervaise)\ **Post date:** [October 19, 2005, 7:39pm UTC](https://boards.straightdope.com/t/knowledge-without-proof/326040/117 "2005-10-19T19:39:01Z")
When **Kozmik** come back, for the love of God, do **not** bring phi. ---
**Author:** ![Kozmik](https://avatars.discourse-cdn.com/v4/letter/k/8dc957/32.png) [@Kozmik](https://boards.straightdope.com/u/Kozmik)\ **Post date:** [October 19, 2005, 8:23pm UTC](https://boards.straightdope.com/t/knowledge-without-proof/326040/118 "2005-10-19T20:23:24Z")
> [@andros](#): > > The missing term–the real number you’re seeking–is _n_, where _n_ = (2_π_-6). No, it’s a real number. Specifically, one that never terminates. 0.28318531… > [@andros](#): > > It is a real number. Yes. > [@andros](#): > > Why on earth does it shock you that an irrational number–2_π_–cannot be expressed as the sum of two integers? This has nothing to do with that. _ **This has EVERYTHING to do with the fact that π never terminates and the answer, 0 does terminate.** _ π - π = 0 ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [October 19, 2005, 8:27pm UTC](https://boards.straightdope.com/t/knowledge-without-proof/326040/119 "2005-10-19T20:27:59Z")
> [@Kozmik](#): > > This has nothing to do with that. _ **This has EVERYTHING to do with the fact that π never terminates and the answer, 0 does terminate.** _ So? ---
**Author:** ![Lemur866](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lemur866/32/434_2.png) [@Lemur866](https://boards.straightdope.com/u/Lemur866)\ **Post date:** [October 19, 2005, 8:28pm UTC](https://boards.straightdope.com/t/knowledge-without-proof/326040/120 "2005-10-19T20:28:13Z")
No, zero DOESN’T terminate! You just gave 1 significant figure, 0. The real value for zero is 0.000000000000000000000000000000000… Zero never terminates. How do you know that you aren’t really dealing with 0.0000000000000001 unless you do your calculation out to infinite decimal places? You can never write 0 out fully. [Previous page](https://boards.straightdope.com/t/knowledge-without-proof/326040.md?page=5) [Next page](https://boards.straightdope.com/t/knowledge-without-proof/326040.md?page=7)