[ 3 / biz / cgl / ck / diy / fa / ic / jp / lit / sci / vr / vt ] [ index / top / reports ] [ status ]
2023-11: Warosu is now out of extended maintenance.

# /sci/ - Science & Math

File: 102 KB, 828x1068, 1655297781301.jpg [View same] [iqdb] [saucenao] [google]

explain

 >> Anonymous Sun Jun 19 14:09:05 2022 No.14585848 >>145858451. Real numbers only have finite place values (...hundreds, tens, ones, tenths, hundreths...)2. Two numbers are the same if there's no number between them3. Take the difference of 1 and 0.99999..., what do you get? Note 0.0000...1 is not a number, because of rule 1.4. Conclude they're the same number.
 >> Anonymous Sun Jun 19 14:23:45 2022 No.14585868 >>14585845flabby fattie
 >> Anonymous Sun Jun 19 14:32:18 2022 No.14585879 >>145858451. If x - y = 0, then x = y2. 0.000... = 03. 1 - 0.999... = 0.000...4. therefore 1 = 0.999...
 >> Anonymous Sun Jun 19 14:58:09 2022 No.14585937 >>14585848>1. Real numbers only have finite place values (...hundreds, tens, ones, tenths, hundreths...)Are ordinal numbers real numbers? If not, then why not just define something analogous to ordinals that fits between any two expressions of real numbers? i.e. >Note 0.0000...1 is not a number, because of rule 1would be an invalid inference under such a construction, because rule 1 would only prove it to not be a real number.
 >> Anonymous Sun Jun 19 14:59:53 2022 No.14585939 >>14585937Yes, wasn't perfectly exact with that last statement, it would imply it's not a real number, which is the system in which the equality 0.9999... = 1 holds.There's nothing stopping you from putting all the numbers you want between 0.999... and 1 in a different number system, assuming you can be consistent about it.
 >> Anonymous Sun Jun 19 15:28:37 2022 No.14585997 >>14585868Looks more like edema
 >> Anonymous Sun Jun 19 15:42:07 2022 No.14586017 >>14585879What is the largest number that is less than 1?
 >> Anonymous Sun Jun 19 15:55:43 2022 No.14586051 File: 49 KB, 512x512, e08c4fe7-c8f5-4293-ae94-7011968f96f3.png [View same] [iqdb] [saucenao] [google] The number used to define a dedekind cut can be placed in either set
 >> Anonymous Sun Jun 19 16:03:09 2022 No.14586076 >>145858481-0.999... is a number though
 >> Anonymous Sun Jun 19 16:04:03 2022 No.14586080 >>14586076Yeah, zero.
 >> Anonymous Sun Jun 19 16:05:38 2022 No.14586082 >>14586080uhh no? the difference between two different numbers is not zero.
 >> Anonymous Sun Jun 19 16:06:19 2022 No.14586083 >>14586082Then what digits does the difference have?
 >> Anonymous Sun Jun 19 16:09:01 2022 No.14586090 >>14586083there doesn't need to be a well defined value
 >> Anonymous Sun Jun 19 16:09:41 2022 No.14586091 >>14586090So your definition of subtraction can lead to undefined values? Seems... like a crappy definition.
 >> Anonymous Sun Jun 19 16:12:44 2022 No.14586100 >>14586091the expression doesn't have to be solvable in regards to containing defined digits or symbols in current math notation for it to be valid
 >> Anonymous Sun Jun 19 16:13:51 2022 No.14586104 >>14586100It does for it to qualify as a real number. Every real number can be defined in terms of a (not necessarily unique) digit sequence.
 >> Anonymous Sun Jun 19 16:21:24 2022 No.14586120 >>14586104ok what digits does pi have? write the whole sequence out big boy.
 >> Anonymous Sun Jun 19 16:23:00 2022 No.14586126 >>14586120It starts like 3.141 and can be derived from any number of infinite sequences to arbitrary depth, unlike your "undefined" answer to 1 - 0.9999...
 >> Anonymous Sun Jun 19 16:29:05 2022 No.14586133 File: 2.42 MB, 498x675, 777473.gif [View same] [iqdb] [saucenao] [google] >>145860170.999...8
 >> Anonymous Sun Jun 19 16:31:04 2022 No.14586135 File: 54 KB, 474x585, 1575268180163.jpg [View same] [iqdb] [saucenao] [google] >>14586133dark matter did it
 >> Anonymous Sun Jun 19 16:31:19 2022 No.14586138 >>14585848>1. Real numbers only have finite place valuesArbitrary rule that has no basis>2. Two numbers are the same if there's no number between themBut there's a number between 1 and 0.999..>3. Take the difference of 1 and 0.99999..., what do you get? Note 0.0000...1 is not a number, because of rule 1.Yes it is, you're just making shit up on the go>4. Conclude they're the same number.Except they're not
 >> Anonymous Sun Jun 19 16:34:04 2022 No.14586149 >>14586138>my made up rules are less arbitrary than your made up rules, wahh
 >> Anonymous Sun Jun 19 16:37:52 2022 No.14586164 File: 55 KB, 601x601, 145234891564.jpg [View same] [iqdb] [saucenao] [google] >>14586149Yes?Since it's not applicable to reality it is clearly wrong, you can divide things into three parts without any problem but you can't here because our mathematical system is archaic and very flawed, you'll actually notice a lot of shit doesn't add up if you go outside and look around a little, you can't just say two things are the same when there is a very defined difference between them.
 >> Anonymous Sun Jun 19 16:38:48 2022 No.14586168 >>14586164>implying math needs to relate or apply to the universe to be validThis is your brain on physics
 >> Anonymous Sun Jun 19 16:41:17 2022 No.14586175 File: 60 KB, 642x792, 1488258403610.jpg [View same] [iqdb] [saucenao] [google] >>14586168>a language which is entirely based on describing the physical dimensions and properties of reality needs to relate or apply to realityYes, retard
 >> Anonymous Sun Jun 19 16:42:31 2022 No.14586179 >>14586175>a language which is entirely based on describing the physical dimensions and properties of realityThat's not what math is you assburger, that's literally describing physics.The vast majority of PhD math has no application or relation whatsoever to reality. Deal with it.
 >> Anonymous Sun Jun 19 16:43:02 2022 No.14586180 0.333... * 3 = 0.999...1 / 3 = 0.333...3 / 3 = 1 = 0.999...
 >> Anonymous Sun Jun 19 16:46:47 2022 No.14586193 >>14586180ok, now prove that 1/3 = 0.333...
 >> Anonymous Sun Jun 19 16:47:51 2022 No.14586195 >>14586179Math and physics are interchangeable dumb faggot, they're two sides of the same coin>The vast majority of PhD math has no application or relation whatsoever to realityThat's literally what I said in my previous post, most mathematics is just retards like you jerking eachother off for nothingBut guess what, 0.999... isn't 1 no matter how much cum you guzzle
 >> Anonymous Sun Jun 19 16:48:01 2022 No.14586197 >>14586193You put your left foot inYou take your left foot outYou put your left foot inand you shake it all about
 >> Anonymous Sun Jun 19 16:52:50 2022 No.14586202 >>14586195There's literally math that you're claiming isn't valid because you're bringing physics into the conversation. The math works, no matter how much you don't like it, and no matter that it doesn't line up perfectly with reality.Math doesn't give a shit about reality, only logical self-consistency. There is plenty of math that is useless for describing objects in our universe. That math is still valid math, even if it you think it's stupid.
 >> Anonymous Sun Jun 19 16:56:09 2022 No.14586212 >>14586193Base 121/3 = 0.4Rational result.
 >> Anonymous Sun Jun 19 16:58:34 2022 No.14586217 File: 21 KB, 320x320, 65925135.jpg [View same] [iqdb] [saucenao] [google] >>14586202>There is plenty of math that is useless for describing objects in our universe. That math is still valid mathNo it's not
 >> Anonymous Sun Jun 19 17:01:45 2022 No.14586224 >>14586217>physics and math are the same if you just pretend all the other non-physics math isn't realYou're a fucking genius, your fields medal is in the mail.
 >> Anonymous Sun Jun 19 17:02:16 2022 No.14586227 >>14586126where is it defined that a real number has to be able to be placed on the number line on a specific spot?
 >> Anonymous Sun Jun 19 17:04:07 2022 No.14586230 File: 213 KB, 2000x1333, 1536641996927.jpg [View same] [iqdb] [saucenao] [google] >>14586224>things that don't apply to reality aren't realYes, retard
 >> Anonymous Sun Jun 19 17:05:48 2022 No.14586236 >>14586230Math isn't real. Hate to break it to you. Not sure who told you otherwise.Math is not real.
 >> Anonymous Sun Jun 19 17:06:27 2022 No.14586239 >>14586230>The physical world constitutes the whole of realityMaterialists shoo shoo
 >> Anonymous Sun Jun 19 17:06:50 2022 No.14586240 >>14586227"where is it defined that numbers have a value"holy fuck anon
 >> Anonymous Sun Jun 19 17:10:04 2022 No.14586247 >>14585845>ifA.BBB... = C>thenC - D = A.BBB...E?
 >> Anonymous Sun Jun 19 17:10:31 2022 No.14586249 >>14586227Various ordering properties imply it.The Archimedean property implies that, for any real number x, there is an integer n such that n <= x <= n+1.You can iterate this implication to show that you can bound any real number to an arbitrary accuracy of digits.
 >> Anonymous Sun Jun 19 17:20:35 2022 No.14586279 File: 1.03 MB, 321x200, 123.gif [View same] [iqdb] [saucenao] [google] >>14586239>he thinks his shitty alice in retardland calculations are applicable in explaining metaphysics when it can't even divide something into three parts
 >> Anonymous Sun Jun 19 17:23:08 2022 No.14586285 >>14586249ok and? one can place 1-0.999... at 0.0001 then 0.00001 etc. depending on the needed accuracynot my problem some boomers didn't consider '...' when writing their deprecated proofs nor that the standard math signature doesn't define a functional symbol for this use case.
 >> Anonymous Sun Jun 19 17:24:43 2022 No.14586288 >>145858451/inf=0
 >> Anonymous Sun Jun 19 17:24:50 2022 No.14586289 >>14586285>one can place 1-0.999... at 0.0001 then 0.00001 etc. depending on the needed accuracyWhich implies that every finite place value will be zero in the full expansion, which makes the number zero.There are extended number systems where what you're saying is possible, but it's not possible in the reals, that sequence converges to zero and only zero.
 >> Anonymous Sun Jun 19 17:26:01 2022 No.14586293 >>14586289>Which implies that every finite place value will be zero in the full expansion, which makes the number zero.I don't see why it would imply that.
 >> Anonymous Sun Jun 19 17:29:31 2022 No.14586307 >>14586293You're saying something like this:1 - 0.999... < 0.00011 - 0.999... < 0.000011 - 0.999... < 0.0000011 - 0.999... < 0.0000001etc.If you pick any place value in the number 1 - 0.999... (e.g. the hundredths place), then one of the above statements forces the digit there to be 0, (e.g. 1 - 0.999... < 0.0001).Since you can pick any place value and conclude it must be 0, it means all the place values are 0.
 >> Anonymous Sun Jun 19 17:31:28 2022 No.14586312 This entire conversation is fussing about the limitations of base 10.In base 12, 1/3 equals 0.4The entire conversation ceases to exist.
 >> Anonymous Sun Jun 19 17:32:52 2022 No.14586315 >>14586312Ah, but instead we have 1 = 0.BBBBBBBBB... in base 12
 >> Anonymous Sun Jun 19 17:35:29 2022 No.14586321 None mentioned that 0.9999.... is a geometric series?
 >> Anonymous Sun Jun 19 17:36:42 2022 No.14586323 >>14586307I don't think so. For any decimal place n that you pick on the right hand side there will be a decimal place n+1 that is equal to 1 on the left hand side.
 >> Anonymous Sun Jun 19 17:41:12 2022 No.14586333 >>14586323Yes, for a finite n, and as n gets higher the zeros push that 1 further down in place value and it disappears in the limit because everything is eventually replaced with zeros.There's infinitely many of those inequalities so you need to let n go infinite.
 >> Anonymous Sun Jun 19 17:48:53 2022 No.14586351 >>14586315What fraction is that
 >> Anonymous Sun Jun 19 17:58:27 2022 No.14586372 >>14586351B = 11 in base 12 by convention, so0.BBBBBBBB... = 11/12 + 11/12^2 + 11/12^3 + ...
 >> Anonymous Sun Jun 19 18:22:31 2022 No.14586418 File: 309 KB, 1200x1487, Microwavetime_95eaa3_7096156.jpg [View same] [iqdb] [saucenao] [google] >>14586212Is 4×12-1 equal to Σ(3×10-1i, i, 1, ∞)?
 >> Anonymous Sun Jun 19 18:25:00 2022 No.14586425 >>14586418Sorry, 4×12^(-1) andΣ(3×10^(-1i), i, 1, ∞). 4chan ruined my superscripts.
 >> Anonymous Sun Jun 19 19:58:47 2022 No.14586651 >>14586333>because everything is eventually replaced with zeros.But it's not because there's a 1 at the end of it
 >> Anonymous Sun Jun 19 20:14:25 2022 No.14586677 >>14585879>3. 1 - 0.999... = 0.000...wrongit's .0...1
 >> Anonymous Sun Jun 19 20:16:39 2022 No.14586682 File: 8 KB, 1098x182, Untitled.png [View same] [iqdb] [saucenao] [google] from a practical standpoint an even weaker claim is truethat's all that matters>mathrannies btfo
 >> Anonymous Sun Jun 19 20:32:28 2022 No.14586727 >>14586333if we can have 1 at n=infinite on the right hand side then that is the number we are looking for to equal 1-0.999...
 >> Anonymous Mon Jun 20 01:39:46 2022 No.14587498 >>14585937What you are referring to are called surreal numbers and are literal joke in math. No one uses them for any real or indeed "un-real" purpose, they are purely wank.I hope this answers your question.
 >> Anonymous Mon Jun 20 01:41:59 2022 No.14587505 >>14587498>they are purely wankIn this instance I'd call it more of a shitpost.
 >> Anonymous Mon Jun 20 01:42:28 2022 No.14587507 >>14586285damn>>14586289won that debate
 >> Anonymous Mon Jun 20 01:48:15 2022 No.14587519 >>14587498Also I am genuinely curious whether ordinals are real numbers.
 >> Anonymous Mon Jun 20 01:51:04 2022 No.14587520 >>14586133I see, I guess I never realized that 8+1=10
 >> Anonymous Mon Jun 20 02:07:14 2022 No.14587541 >>14586017There is none. If one chooses any number less than 1, we can always choose a number higher than that, but still less than 1. Let's say X is the largest number less than 1. Then we see that 1 > (1 + X)/2 > X (that is, we have a new "largest number less than 1"), which is a contradiction of our assumption.
 >> Anonymous Mon Jun 20 02:28:45 2022 No.14587573 >>14587541That is just a giant cop out, and is like saying 1=2 in integers because nothing exists between them.
 >> Anonymous Mon Jun 20 02:43:35 2022 No.14587596 Because 0.999… =/= 0.999…9
 >> Anonymous Mon Jun 20 07:59:32 2022 No.14587994 File: 13 KB, 987x303, numberretard.png [View same] [iqdb] [saucenao] [google] >>14586682this is the most retarded take in the entire thread
 >> Anonymous Mon Jun 20 10:24:17 2022 No.14588126 >>14585845This made me realize how retarded most mathematicians are. It's not even about whether it's true or not. It's that all the popular proofs are so obviously wrong but still taught in school and textbooks everywhere.
 >> Anonymous Mon Jun 20 10:25:43 2022 No.14588127 >>14588126Wrong how?
 >> Anonymous Mon Jun 20 10:28:09 2022 No.14588128 0.9999... is NOT equal 1 but it is quite close. So, we can make an approximation. We can say, 0.9999... is approximately equal to 1. Like this,0.9999...≈ 1
 >> Anonymous Mon Jun 20 10:30:03 2022 No.14588132 >>14588127Depends on the proof. Pick one of the popular ones and I'll tell you.
 >> Anonymous Mon Jun 20 10:32:13 2022 No.14588136 >>14585845Precision problem, what else is to explain. For an infinite periodic 0.9999..., it is unironically and practically 1
 >> Anonymous Mon Jun 20 16:28:24 2022 No.14588689 >>14588128The problem comes from conversion across asymptots using a different convention.9/9 = 0.999... = 1 = 1/1Following this convention1/10 = 0.19/10 = 0.9 99/100 = 0.99999/1000 = 0.999999.../1000... = 1?
 >> Anonymous Mon Jun 20 16:56:31 2022 No.14588745 >>14588689>999.../1000...inf/inf is undefined
 >> El Arcón Mon Jun 20 16:57:28 2022 No.14588746 Was it the food or the water?
 >> Anonymous Mon Jun 20 16:58:56 2022 No.14588752
 >> Anonymous Mon Jun 20 17:12:31 2022 No.14588777 >>14588745then 9/9 is undefined as well...Is 0.111.../0.111... undefined as well, even though its 1/9/1/9?
 >> Anonymous Mon Jun 20 17:16:07 2022 No.14588782 >>14588745>>14588777Said another way:x ^ (1/n) approaches 1, but is never 1.
 >> Anonymous Mon Jun 20 17:17:32 2022 No.14588785 >>14588782This can be shown experimentally with:(x ^ 2) ^ 0.5 does not equal (x ^ 0.5) ^ 2
 >> Anonymous Mon Jun 20 17:18:48 2022 No.14588787 >>14588689>999.../1000... = 1?999.../1000... = 0.999...
 >> Anonymous Mon Jun 20 17:22:24 2022 No.14588796 >>14588787So 999.../10000 = 0.999...But 999.../999... = 1?
 >> Anonymous Mon Jun 20 17:24:08 2022 No.14588798 >>14588796This would mean that 9 * 0.111... = 1?You see there is a fundamental flaw here.
 >> Anonymous Mon Jun 20 17:31:53 2022 No.14588810 >>14588777>then 9/9 is undefined as well...for you, sure
 >> Anonymous Mon Jun 20 17:34:17 2022 No.14588819 >>14588810So then 9 * 1/9 = undefined?
 >> Anonymous Mon Jun 20 17:35:37 2022 No.14588821 >>14588819for you, sure
 >> Anonymous Mon Jun 20 17:51:20 2022 No.14588866 >>14585845They're equal because we define them as equal within our number system
 >> Anonymous Mon Jun 20 17:51:35 2022 No.14588868 >>14587519Anybody? Bueller?
 >> Anonymous Mon Jun 20 22:32:26 2022 No.14589659 >>14588752What you link is correct. But it doesn't prove $0.\bar{9}=1$.
 >> Anonymous Mon Jun 20 23:57:40 2022 No.14589859 >>14589659aww it's retarded
 >> Anonymous Tue Jun 21 00:07:09 2022 No.14589884 >>14586727>>14586651As soon as you start trying to put digits at the "infinityth" place you're no longer operating under the rules of the real number system. Either you ditch that system or work inside of it, but you can't have a real number that has a one at n=infinity.
 >> Anonymous Tue Jun 21 00:16:22 2022 No.14589901 >>14589884*cough*1/9
 >> Anonymous Tue Jun 21 00:20:42 2022 No.14589972 >>14589901Still doesn't have a 1 at the "infinityth" place. The concept of "infinityth" place value has no meaning in the real numbers. For example, what's the "infinityth" place value of Pi, or 1/7?
 >> Anonymous Tue Jun 21 00:25:09 2022 No.14589984 File: 39 KB, 650x340, k.jpg [View same] [iqdb] [saucenao] [google] >>14589972so it's a 3 then, got it
 >> Anonymous Tue Jun 21 00:26:01 2022 No.14589986 >>14589984lol, whatever you say anon