It's simple. There are only so many variations with 0 through 9 that can be made. It's bound to repeat a pattern. You cannot get anything infinite from a finite source.
RiderFan said: It's simple. There are only so many variations with 0 through 9 that can be made. It's bound to repeat a pattern. You cannot get anything infinite from a finite source.
@RiderPan Seriously, you are forgetting one particular: there is no limit on length. There a finite number of patterns for every length, but there is an infinite number of patterns counting every possible length.
Just think: Being A a finite set of all patterns as you said. Since A is finite there at least one pattern that is the longest. I take that pattern and I can make a new pattern just putting in juxtaposition a new digit. The resulting pattern is one longer of the longest of A, then it is not in A. I means that A does not contains all patterns or it is not finite.
Anyway, feel happy to believe what you like.
After `4 times the arctangent of 1' I'll say: Four times the integral between zero and 1 of the square root of one minus x squared in dx! We all love pi :D
#Thomas, no one forced you think about the problem. But I guess the idea of fun is different for everyone.
@skizzilini, I think RiderPan was playing dumb. Moreover, pi is not simply irrational (as is the square root of 2), but also transcendental: it means that pi is not a solution of any polynomial with integer coefficients.
Danbooru has always been such a great place. You can learn so much here, you don't even need to go to school. From what I learn here, the answer to everything is ⑨.
RiderFan, you're a bro and all, but give it up. Math, specifically the stuff linked to above, proves pi is irrational (i.e. it doesn't end and it doesn't repeat itself).
That's not "thinking about it." You're just re-stating your premise without evidence. Why must it eventually repeat? Any pattern can be altered by the addition or subtraction of a single digit. And the length of said pattern can always increase.
I thought about RiderFan's statement and he might be meaning something different from what we usually understands about repetition of a decimal number.
PI does have repeating patterns in it, for example 123123 occurs at position 263177 (according to etb's website). Since PI is an infinite irrational number, it may be that any sequence of number can be found in it. (I know no proof of this, just guessing) Then even a highly repetitive sequence can be found in PI.
Taken even more 9ly, PI repeats at the 3rd digits after the decimal, when the number '1' is repeated.
In conclusion, PI does not repeat, sequences of numbers do repeat inside PI, and finally RiderFan is really stupid.
you are making such a big woss about something so easy to prove wrong. He is talking about something that repeats, look at this. 0.121121112111121111121111112 It may look kinda dumb, but there is a "pattern" but it wont repeat, since you always add something in the middle. if you go further on the number you will just find a thousand 1 and a 2 in the end. the only thing that repeats itself here, its the "12" at the end of a sequence of 1.
Jesus, that pi is a definable function is not the point, Pi is non-repeating and irrational. The full exact value can't be known. We can know the value to any useful degree of certainty. There are functions to generate it. Pi is defined by the functions that use it, and vice versa, including its geometric origins.
If you say .121121112... Yes, it's a non-repeating function. You can express it easily enough as a function.
Repeating numbers like .33333... = 1/3 and .99999... = 1 are exact.
As far as we currently know, Pi not only is not exact, but has been proven to be impossible to know exactly.
Think about how fucking crazy irrational numbers are: e^(i*Pi) = -1
e, also irrational, 2.71 something to the power of...
The value of the squareroot of -1, what the fuck is that? times Pi, 3.14 something
= -1 exactly. What the hell.
It's only exactly -1 if you round unnecessarily, or use the exact formulas that are used to generate those numbers.
You can't put in 2.71^(sqrt(-1))3.14 and get 1. You can't even begin to do it by hand unless you're in your third semester of calculus.
On the gripping hand, it's quite easy to calculate pi to a degree that it is known to such a degree as to be less of a factor than any other source of error in your work.
Dr_Fine_Rolo said: Jesus, that pi is a definable function is not the point, Pi is non-repeating and irrational. The full exact value can't be known. We can know the value to any useful degree of certainty. There are functions to generate it. Pi is defined by the functions that use it, and vice versa, including its geometric origins.
If you say .121121112... Yes, it's a non-repeating function. You can express it easily enough as a function.
Repeating numbers like .33333... = 1/3 and .99999... = 1 are exact.
As far as we currently know, Pi not only is not exact, but has been proven to be impossible to know exactly.
Think about how fucking crazy irrational numbers are: e^(i*Pi) = -1
e, also irrational, 2.71 something to the power of...
The value of the squareroot of -1, what the fuck is that? times Pi, 3.14 something
= -1 exactly. What the hell.
It's only exactly -1 if you round unnecessarily, or use the exact formulas that are used to generate those numbers.
You can't put in 2.71^(sqrt(-1))3.14 and get 1. You can't even begin to do it by hand unless you're in your third semester of calculus.
On the gripping hand, it's quite easy to calculate pi to a degree that it is known to such a degree as to be less of a factor than any other source of error in your work.
Oddly enough, there is a location in pi known as the Feynman Point, located at the 762nd digit past the decimal point. At this point, there is a sequence of six ⑨s. The probability that this sequence would occur so (relatively) early in a random sequence of numbers is about 0.0008.
...I can't help but think that Cirno has something to do with it...
Well...if Quantum Mechanics has anything to do with it If the Planck Length is indeed the smallest increment this universe can be measured in, from a pure mathematical standpoint that Pi really is infinite. But at some point, what makes the circumference of a circle reach a mating point must mean that Pi Must have an ending value. piss poor Highschool level logic but thats been my though on Pi
Virgorival said: Well...if Quantum Mechanics has anything to do with it If the Planck Length is indeed the smallest increment this universe can be measured in, from a pure mathematical standpoint that Pi really is infinite. But at some point, what makes the circumference of a circle reach a mating point must mean that Pi Must have an ending value. piss poor Highschool level logic but thats been my though on Pi
That only works if you ever find an actual circle in the physical world. And I mean the perfect geometric construct formed by the set of all points on a two dimensional plane equidistant to one defined point, not an object shaped like a circle or with a circular looking drawing on it. Ceci n'est pas une pipe.
Either she found the Feynman point (6 9's actually exist in sequence in Pi (base 10) at the sevenhundreth-something number), or she clearly has intelligence, but not wisdom. Lindemann-Weierstrasz-theorem. (It basically says: e^a is transcendental for algebraic a. Because e^pi*i=-1 and -1, i are clearly nontranscentental, pi must be that.) The LW theorem is kind of... complex so just find a proof on wikipedia or something.
Virgorival said: Well...if Quantum Mechanics has anything to do with it If the Planck Length is indeed the smallest increment this universe can be measured in, from a pure mathematical standpoint that Pi really is infinite. But at some point, what makes the circumference of a circle reach a mating point must mean that Pi Must have an ending value. piss poor Highschool level logic but thats been my though on Pi
Actually, assuming an infinite universe, pi would not be finite even considering the Planck Length. A circle with radius approaching infinity would be able to yield infinitely more precise values for Pi that still applies to the definition of pi as the circle constant.
RiderFan said: Final thought on my part: Think about it, given a set amount of numbers it will eventually repeat.
Your theory is similar to the theory that, on a larger scale, all chaos/random phenomena is ordered/patterned (which is, to an extent, true), but this is given a specific scale - a finite value. Given infinity, this is insinuating that it will "end up" as a repeating number. Segments of the string of digits in pi will repeat, yes, but in an ultimately imperfect, and therefore non-patterned fashion. If pi were to ever, as its number of digits approached infinity, began to fall into a definable pattern, then it would no longer be an irrational number. As etb put it, as more digits are added, the number of possible values to be "added" to the end of the string will grow faster than the probability that any part, much less all of, the string of digits will repeat.
Look at the Leibniz formula for pi and you'll see that there's no way it could repeat. It's a sum of fractions with ever-increasing denominators, and it goes on forever. No repeating decimal, just a sequence of digits that looks almost random.
We've arguably been pointing these things out for RiderFan's benefit, but that person hasn't commented on this post in almost a year, so who knows if the lesson has been learned or not.
GreenDrag said: Pi might be, in decimal system irrational, however it isn't in base 9, as proven by professor Cirno.
Nice try, but irrational numbers, by definition, cannot be formed out of a fraction composed of two integers. Every integer in any one base has a representation in every other base, hence irrational numbers are irrational, regardless of base. (if you're curious, the first 9 digits of pi in base 9 are 3.12418812.)
With all due respect sir, if we reverse the polarity of the power source feeding the quantum crystal lattices, it will destabilize the waveform propogation and cause a feedback loop in the alpha particle conversion system. Who knows what the ramifications might be?
Actually, infinite again, sorry. With a base 11 system, there's 11 possible digits. It's in fact technically feasible, though practically useless, to create a base infinity number system: every expressible number would have it's own symbol.
Etaoin said: Actually, infinite again, sorry. With a base 11 system, there's 11 possible digits. It's in fact technically feasible, though practically useless, to create a base infinity number system: every expressible number would have it's own symbol.
I'm not sure where you're from, but here we use base 10.
Virgorival said: Well...if Quantum Mechanics has anything to do with it If the Planck Length is indeed the smallest increment this universe can be measured in, from a pure mathematical standpoint that Pi really is infinite. But at some point, what makes the circumference of a circle reach a mating point must mean that Pi Must have an ending value. piss poor Highschool level logic but thats been my though on Pi
Late reply is late so I keep it short: Things like electromagnetic waves are perfect circles and require the exact PI. And you have cross-interference.
Etaoin said: Nice try, but irrational numbers, by definition, cannot be formed out of a fraction composed of two integers. Every integer in any one base has a representation in every other base, hence irrational numbers are irrational, regardless of base. (if you're curious, the first 9 digits of pi in base 9 are 3.12418812.)
umm, pi in base pi is 1..... in some bases irrational numbers are rational namely bases that are contrived to the irrational number IE Pi, 1/2Pi 2Pi
dusparr said: umm, pi in base pi is 1..... in some bases irrational numbers are rational namely bases that are contrived to the irrational number IE Pi, 1/2Pi 2Pi
actually, since in base 9, 9=>10, and in base 7, 7=>10 then in base pi, pi=>10, not 1. 1 in base pi is still 1. I find it irrational of you to forget an important digit in your answer.
dusparr said: umm, pi in base pi is 1..... in some bases irrational numbers are rational namely bases that are contrived to the irrational number IE Pi, 1/2Pi 2Pi
As mentioned by Ariri, 1 in base pi is still 1, because (using the common notation) the ones place in any number base represents the base to the power 0, which is always 1. If, as suggested, you mean 10, I would call to attention the fact that 10 in base pi is not in fact an integer. If this seems counter-intuitive, that's what you get for working in a non-integer base.
It makes more sense with Kanji or Roman numerals. I + I = II. Nobody should need that explained. It's why 1+1=11 is a funny funny joke when you're eight years old. You have one of something, now here's another, we call that two because Latin used "duo" and Old English used "tu".
So what I have read. Marisa in fact recited Pi Twice as she was on her broom going to someplace in one of the games...or stories. So in fact if Crino for figuring it out. Maybe isn't too hard to realize.
Master_Snipe said: So what I have read. Marisa in fact recited Pi Twice as she was on her broom going to someplace in one of the games...or stories. So in fact if Crino for figuring it out. Maybe isn't too hard to realize.
That was in Mountain of Faith, before fighting Hina.
As for pi, it has now been calculated to ten TRILLION digits. The last one for now is a 5.
Shintear said: Not just that. The difference between ANY two points on the number-line is infinite. That's awesome, right?
False, the difference between 1 and 1 is zero, or the difference between any two points on the number-line that are equals is zero. If A=1, then their difference is zero. Now, if A!=1, then yes, their difference is infinite.
Co250 said: Can someone please explain to me why 1 + 1 = 2 ? yes, I am asking it seriously
etb said: A possible definition of sum of natural numbers is: a + 0 = a a + s(b) = s(a) + b
where s means successor. So if you get 1 + 1 that is s(0) + s(0) you have: s(0) + s(0) = s(s(0)) + 0 = s(s(0))
Of course you never say twice the successor of 0, you simply say 2.
If you would like a more stringent proof, I will point you in the direction of the Principia Mathematica by Whitehead and Russel. By page 86 of the second volume you will have the full proof that 1 + 1 = 2, accompanied by the rather infamous quotation "The above proposition is occasionally useful."
personman23 said: Pi=NotPi? Thats both simple, and infinitely difficult. Shouldn't be a problem really...I think...
P is the set of all decision problems (a question that can be answered with yes or no) that can be solved in polynomial time. NP is the set of all decision problems whose solutions can be verified in polynomial time. The question asks "for ALL problems whose solutions can be verified quickly, is it ALWAYS possible to find an algorithm capable of solving it quickly as well?" It is currently thought to be false, but no proof exists either way.
Chibi_Musashi said: False, the difference between 1 and 1 is zero, or the difference between any two points on the number-line that are equals is zero. If A=1, then their difference is zero. Now, if A!=1, then yes, their difference is infinite.
Wrong. It's true that between any two different elements of the real set there exist infinitely many other elements (this is also true of the rational and irrational sets), but the difference between any two elements of the set has to be finite, or the real set wouldn't be a field. 2-1=1, and 1 isn't infinite.
450AHX said: Wrong. It's true that between any two different elements of the real set there exist infinitely many other elements (this is also true of the rational and irrational sets)...
I failed in what I tried to say, i meant that by saying their difference is infinite. you cant count how many elements there are between two different numbers.
