I know this is a common bait question , but I don't say this to be toxic , I just need to use all the number spacesIts for a personal thing.
0.999 repeating is mathematically identical to 1
>>16791861Ok Einstein then explain this[math]\sum_{n=1}^{\infty}9/10^{n} + \sum_{n=\infty}^{1}1/10^{n} = 0.999... ...111[/math]
>>16791912n = infinityis that possible? how can you start at infinity?
>>16791912Sure, that statement is false and you're an idiot.
>>167916761/3 ≠ 0.333...That's because 0.999...+R for remainder R, divided by three is 0.333...+R/3
>>16791912You can also swap the sum and get 0.111... ..999, which shows an obvious truth that mathematicians ought to be honest about: addition is not communicative nor associative with infinity, yet they use such commutativity and associativity to make these absurd claims that 0.999... = 1
>>16791912>>16791962Since when was addition the same operation as concatenation?
>>16791973You just made that up. It's like 2 cars, driving at infinite speed, that are about to crash, but never crash. Or do they?
>>16791861yea I want the oposite somehow , were I repeat like 999999.......from the left. but its still identical to 1 so I can use all the space fields in numbers , do you know of a similar logic that I could use.
>>16791676Base 3Simple proof :Reminder that 1[base 10] = 1[base 3] = 1 in any base (base >1 obviously).1/3[base 10] = 0.1[base 3]3[base 10] = 10[base 3]3[base 10] * 1/3[base 10] = 10[base 3] * 0.1[base 3]3/3[base 10] = 1[base 3] = 1 (any base)Simple as.
>>16791676this is what I am looking for , just to get 1 or 2 by just repeating all posible math spaces with 9. is their some kind of trick , because as far as I know the same logic that allows , .99999....= 1 , doesn't yell well with the idea that 99999......= 1 , but I need to figure out something.
>>16792036I need somekind of autistic jewish math trick to save me out of this one.
>>16791973you tell me. the claim is that sum (1/10^n) = 0.9 + 0.09 + 0.009 which gets concatenated into 0.999...funny how you apply that criticism to the 0.999... != 1 crew but not to the 0.999 ... = 1 crew.
>>16792036>doesn't yell well with the idea that 99999......= 1 , but I need to figure out something.Are you looking for 10-addic numbers ?x = ...999999.0x + 1 = ...99999.0 + 1x + 1 = ...00000.0x = -1 = ...999999.0...9999.0 = -10.9999... = 1...9999.0 + 0.9999... = ...999.999... = 0
>>16792065I am trying to find a way to use all the numbers to equally represent the number line , in the same way that an autistic nerd could tecnically say "give me 0.99999........ icecubes" to mean one , that uses more symbols than 1. it uses all the 9s posible to the right , I want to do something similar to all the real numbers and also to the left somehow.
>>16792081*all the number spaces.
>>16792081Like this ?0.999...8 or 0.999...x, x can be Pi, e, a rational, whatever, are all equals to 1.0.999...8 = 0.8 + 0.1999...80.999...8 = 0.8 + 0.18 + 0.018 + 0.0018 + 0.00018 + ...0.999...8 = 0.8 + 2*(0.09 + 0.009 + 0.0009 + 0.00009 + ...)0.999...8 = 0.8 + 2*(0.0999...)0.999...8 = 0.8 + 2*(0.1)0.999...8 = 1It works with whatever the 0.999...x ends :0.999...3 = 0.3 + 0.6999...30.999...3 = 0.3 + (0.63 + 0.063 + 0.0063 + 0.00063 + ...)0.999...3 = 0.3 + 7*(0.09 + 0.009 + 0.0009 + 0.00009 + ...)0.999...3 = 0.3 + 7*(0.0999...)0.999...3 = 0.3 + 7*(0.1)0.999...3 = 1
>>16792089.99999 is perfectly fine , I am more so just looking for the logic that whould allow me to do that in its oposite direction , I heard of pedriatic numbers before but as far as I know they don't have a number line , so that might not work out as well.basically some kind of matematical logic that would make an infinite amount of whole 9s to the left equal 1. se pick for it
>>16792108>but as far as I know they don't have a number lineThere are.Check "mapping p-addic number projection".
>>167916761/3 does not equals 0.33... nor it equals 0.33...3 .Neither of those two things are decimal numbers nor rational numbers, so the comparision is undefined.You can say 0.33...3 is a hyperreal (hyperdecimal) number that is different from 1/3 by 0.00...3 (a infinitesimal but non-zero value).A simple way to construct hyperreals is to say 0.33..3 is a sequence of {0.3, 0.33, 0.333, ...} and various operations betweens them are defined pointwise. 1/3 - 0.33...3 = {1/3 - 0.3 = 0.0(3), 1/3 - 0.33 = 0.00(3), ...}.This way 0.99...9 is also not a decimal number but hyperdecimal number and it doesn't equals to 1.>>16791912You've got infinities wrong, and it is easy to show in nonstandard analysis.If we say your infinity sign in both sums is the same hypernatural \omega, then result of your expression is a hyperreal, say, x.Like I've explained above, hyperreals and hypernaturals can be thought of as sequence of approximations of infinitive or inifnitesimal numbers.So you can compute N-th item of the sequence x by using N-th item of \omega sequence. You can pick any sequence diverging towards positive infinity for \omega, let's take\omega = {1, 2, 3, ...} .Then we get:x[1] = 9 / 10^1 + 1 / 10^1 = 10 / 10^1x[2] = 9 / 10^1 + 9 / 10^2 + 1 / 10^2 + 1 / 10^1 = 1.1x[3] = 9 / 10^1 + 9 / 10^2 + 9 / 10^3 + 1 / 10^3 + 1 / 10^2 + 1 / 10^1 = 1.11So x = {1, 1.1, 1.11, 1.111, ...}, and x != 1.(1)>>16791962> addition is not communicative nor associative with infinityYou *can* rearrange sums of the infinitive sequences if you don't mishandle (skip) any of the "infinitiveth" elements (the ones at \omega, \omega - 1, \omega - 2, \omega - [[any natural number]] if the length of the sequence is \omega).
If you restrict yourself to repeating patterns, both infinite decimals and 10-adics get restricted to the rational numbers. So you can easily define the notation to mean the 10-adic number to the left of the decimal point plus the decimal number to the right. For example ...999.999... = ...999 + .999... = -1 + 1 = 0.
>>16792179I was think about that and was gonna ask about it here so thank you anon. but the what is the number that .....99999 in pediatic numbers is , is it -1 , if so thats great specially , but I do want to ask for more precision. see pic here
>>16792168this might sound wierd , but I don't particularly argree with 0.999... = 1. but I see the logic as interesting , and as such I am asuming its true for a thing I am making.
>>16791676no and yes, you can't have both sides of the dot have infinite places, but you can have infinite to the left and finite to the right, which gives you the p-adics, with stuff like ...9=-1
>>167916760.3333...3 is the closest approximation to 1/3, but it is not 1/3, you could argue 1/3 is irrational since no such thing as a perfect third of something can existSince we do not know the true value of 1/3 or 2/3 we represent them as their closest value, but we do know the true value of 3/3 which is 1, three thirds of something is the whole of it
why does this shit filter so many people it's a quirk of the numerical base you're using nobody is dicking around with epsilon reminders in infinity when 1/10 is 0.00011(0011) recurring in base 2 or whatever
>>16792294I forgot pic
>>16792404>quirkFunny way to say broken system. So much for logic...
>>16791676you can whatever the inverse of division is and repeatedly add and divide instead of repeatedly subtracting and multiplying and get the left sided integers to fill up if thats what you’re asking.
>>16792481that is what I am asking , but how does someone do that , what is thee inverse of divition in this context , like multiplication obs not work right?
sorry if I am seeing kind of reterded anons , I am just a little bit tired.
>>16792391> you could argue 1/3 is irrationallmao
>>16792453the price of a perfect system is infinite complexity there are always tradeoffs if you think you can come up with a better numerical system than the current one present your findings to the Nobel Prize committee and be immortalized as the guy who revolutionized mathematics forever.
>>16792486division isnt technically the inverse of multiplication.you can just do 1/-3 and repeatedly add and divide.1-(-3)*3 = 1010/10 = 1do this for every integer place as if you were dividing upwards.
>>16792437Why are there two decimal points in that picture?
Three proves for this:1.According to formal definition for two real numbers to be distinct there must be infinite real numbers between them. In this case leave alone infinite real numbers you can't even name 1 2. Let's take x = 0.9999....Then 10x = 9.99999.....Then 10x-x = 9.99999..-0.9999...9x = 9 Thus x is 13. The one that you showed The last two proofs may seem as an adjustment of rules and compromises to get a false example but using the rigid definition we still get 0.9999... to 1 I'm open to any doubts that you may yield to my logic
>>16792577well I don't exactly know how to represent the change from regular numbers to p-adic numbers , specially since its being doing for none practical , economical , acemical or truthfull reason. I mean its tecnically being math for all of those , but not really.
>>16792590I am taking .9999=1 for granted , my problem is trying to figure out how to abuse a similar thing to get it to the other direction , that way I can use all the number spaces all the time. unfortunatly while I do think anons here have allready given me enough help for my arbritrary problem , and I do mean this fully , a retard wave has hit me today , so a little bit more help would be appreciated anon.
>>16792590This logic is actually wrong.First, 0.9999... is not a real number, nor a rational number, not even a decimal one, because ... is not a digit. Unlike 0.(9) .Depending on how you extend real numbers to allow 0.9999..., you'll get different results. If I use hyperreal numbers (see >>16792168) and nonstandard analysis, then proof 1 and 2 will be wrong. I don't get where third proof is.> 1.According to formal definition for two real numbers to be distinct there must be infinite real numbers between them. In this case leave alone infinite real numbers you can't even name 1 0.9999... is not a real number. Let's define it as a hyperreal.According to the transfer principle, your distinction criteria will look like (*1.1) "for two hyperreal numbers to be distinct there must be *infinite hyperreal numbers between them".There property of set being *infinite is a nonstandard counterpart to property of set being infinite (in standard sense).*infinite may be same as infinite, may be not, depending on how you define it. Let's assume it is not the same property.Now, let's take that there are infinite real numbers between two different real numbers. (I don't want to prove this).More formally, (1.2) for real a and real b > a, set of {x in reals | a < x < b} is infinite.Then, by transfer principle, (*1.2) for hyperreal a and hyperreal b > a, set of {x in hyperreals | a < x < b} is *infinite.By combining (*1.1) and (*1.2) you can say that two hyperreals a and b are distinct if either a > b or b > a.(Lol, and you don't need any transfer principle to say this)As I've shown in >>16792168, 0.999...9 is less then 1 (by an infinitesimal number), thus they are distinct.[Part 1/2]
>>16792963[Part 2/2]>2. Let's take x = 0.9999....>Then 10x = 9.99999.....>Then 10x-x = 9.99999..-0.9999...>9x = 9>Thus x is 1Again, I work in hyperreals.You've skipped an infinitesimal difference at third step.I'll start from real numbers, then go to hyperreals via transfer principle.x = 0.99..[n nines]..99 (with n being a (finite) natural number).10x = 9.9..[n nines]..9010x - x = 9 - 0.0..[n zeroes]..09 = 8.9..[n nines]..919x = 8.9..[n nines]..91x != 1By transfer principle this works for hypernatural (infinite) amount of nines in x. It is still != 1.
>>16792591Do you want to make the last 9 of the 10-addic at left to touch at infinity the last decimal of 9 at right ?Like a full circle ?For me, full circle is related to e^(i*x)Euler pretentious thingy :e^(i*Pi) + 1 = 0It totally looks like :...999.0 + 0.999... = 0With :e^(i*Pi) = ...999.0And :1 = 0.999...The goal I guess is to find the behavior of ...999.0 around the circle e^(i*x) = cos x + i sin x
>>16791912An endless number ends with 111?
>>16792081That's infinity. These two principles are non-symmetrical and hence yield non-symmetrical output object types (a quality like infinity vs a number)
>>16793386>ends with 111...at infinity... after an infinity of 999...It works with any shit :0.999...Pi or 0.999...e
>>16793386It is endless but in the other direction.0,999... Is racing towards inf with infinite speed and 0,... 111 is racing from inf with infinite speed towards 1 but they are infinitly far away so they should never meet.
>>16792391>since no such thing as a perfect third of something can existthe value "20" is a perfect third of the value "60".>inb4 why do you say it as 'value "INTEGER"'I have to be very precise for the slow ones.
>>16793397>0.999...Pi or 0.999...eAre these two different numbers? If yes, please tell me what the value of the number in front of them is (I assume 0.999....0, right?)And if no, what is the purpose of the notation that includes that part in the front?>>16793436Nothing is racing, just like nothing is racing with the number "15". Notation does not denote some process or function. The actual number is independent of notation.
>>16793436number ls "race" with "speed"?where can I read the formal definitions for these properties?
>>16793456>>16793476Yes, numbers race, but people just dismiss it because they are somehow blind to it or think it's not important for the specific problem they try to solve. Assumtion: Every process of drawing/thinking/generating a number takes time.In the realm of mathematics numbers just instantly appear out of nowhere and solutions to calculations are instant.You can do funny things with speed numbers:In 0.999... It takes time t to generate each 9.Another 0.999... may have the speed t/2.The moment you add them they become0.999... + 0.090909.... Because the second one was generated slower, half as fast. Of you model it like it takes time t to count from 0 to 9 so the first number with speed t is 0.999... and the second one with t/2 is 0.(4.5)9(4.5)9... because when a 9 in the first term was generated the second term only was halfway done.You can model this with f. e. sine waves.
>>167919581/3 = 3/10 + 1/30= 0.3 + 1/30= 0.33 + 1/300= 0.333 + 1/3000:= 0.333... + 1/inf= 0.333... + 0= 0.333...
>>16793938that's not a formal definition, try again
>>16793989you're not a formal anything, fuck off
>>16794047Why are you so angry? You don't seem interested in explaining your newly discovered maths but only insult other people.From what I have gathered you seem to have taken a number and added a "fasteness" quality to it, and based on this quality when you add it to another number with a different "fastness" you get a different result from normal addition.So please, given two real numbers x and y, and their speed to calculate each digit called tx and ty, tell me exactly how to sum.
>>16791861Men are academically equal to women. That only matters to people who give it value, but in reality if something isn't 1 it's not 1
>>16794292That guy wasn't me but he is right. Anyway:>So please, given two real numbers x and y, and their speed to calculate each digit called tx and ty, tell me exactly how to sum.1) pick the number with the fastest t, that t is 1. Let's call it t02)any other number in the calculation has t<=1, they are tnSo we can plot them like pic related. In pic related tn = 0.5Which number to add at a specific decimal place you can read from the graph at the whole x values. F.e. the first ist 9+4.5 the second 9+9 then 9+4.5 and so on.You can model this with any other wave like function.
>>16794941I asked you to use x, y, tx, and ty, and to provide a method for summing the two numbers. Instead you completely ignored me, used your own unexplained notation, and posted a meaningless graph. You are worthless
