Omg, trips galore.
>>169747021 – 1/99^2 = 999897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110090807060504030200/(10^(2*99) – 1)
is there an explanation to this phenomena? it's like the gremblins of the math world havin a laff
>>16974725Check out what happens when you divide 16,017 by 20,000.More seriously: you can trivially get any pattern of numbers you want as a decimal by dividing [pattern you want] by [10 times the length of digits in the pattern] then simplify the fraction to obfuscate what you're doing. If you want it to be a repeating decimal, subtract 1 from that denominator before simplifying.Try dividing 23 by 33 to see what I mean.
>>16974898I get the concept but not the exact chain of actions, you cheeky basterds, I like, if you're teachers do one with 67 in it, they'll trip balls
>>16974725[eqn]\frac{1}{x - 1} = \sum_{n=1}^\infty \frac{1}{x^n}[/eqn][eqn]\frac{1}{(x - 1)^2} = \sum_{n=1}^\infty \frac{n}{x^{n+1}}[/eqn]
Some other ones to try: [math]\frac{1}{998}[/math], [math]\frac{1}{998999}[/math]
>>16974725Or to put it in a bit simpler terms:Let x = your number.Then 1000x = your number shifted left 3 digits.Do 1000x - x and you get 999x = 0.(001 repeating).Let y = 999x and do the same thing. 1000y is 1.(001 repeating). So 1000y - y = 999y = 1.
If you plot the digits of 1/63, a sinusoid fits through them perfectly.https://www.desmos.com/calculator/oaushygkek
>>16975378Also works with 1/39.https://www.desmos.com/calculator/2bcxvithbi
>>16975378>>16975382This works for any arbitrary set of data points. That's, like, the whole thing about aliasing.
>>16975393What if my data points are e, pi and pi^e, though?
>>16975395Yes, even that arbitrary data set. In fact, there's infinitely many sinusoids that cross through them
>>16975397>there's infinitely many sinusoids that cross through themBut you were talking about aliasing, not just sinusoids crossing through points.
>>16974725https://www.youtube.com/watch?v=daro6K6mym8
>>16975403Well aliasing refers to the fact that an infinite number of sinusoids cross through a given set of data points. So for every "true" signal, there exists infinitely many "alias" signals. I'm curious what point you're attempting to make here.
>>16975420My point is that I'm retarded. I was thinking A*sin(x*f), which has only two degrees of freedom. But it's actually more like A*sin(x*f+p)+c, which has 4. So I guess I'd need 5 random samples to actually make my point that you can't necessarily even get even one sinusoid to go through them, let alone an infinite number of sinusoids.
>>16975427>So I guess I'd need 5 random samples to actually make my point that you can't necessarily even get even one sinusoid to go through themStill untrue. No matter how many points you have, as long as it's finite, infinitely many sinusoids exist which cross through them.
>>16975430>dumb bioLLM tries to contradict a reasoned argument using vague word associations
>>16975444You didn't make an argument. You made an assertion. I responded with my own assertion (which is actually a well known fact about sinusoids that you can simply google).I'll give you a hint: the frequency of the sinusoid may be much higher than your sampling rate. And the amplitude may be much grater than the range of given values.
>>16975461I did, you're just too mentally challenged to realize it. Hint: you only have as many degrees of freedom as you have degrees of freedom.
>>16975462>you only have as many degrees of freedom as you have degrees of freedom.This does not support your argument.
>>16975469Here's your claim:>there's infinitely many sinusoids that pass through any arbitrary set of data pointsWell, here's my data set.(1, e)(2, pi)(3, e^pi)(4, pi^e)(5, e/pi)In your next post, find at least two sinusoids that pass through these points. Protip: there will be backpedaling, cope and deflection.
>>16975472I concede. I am stupid and was thinking about something else entirely.
>>16975521Ok. Since you're being decent about it I'll admit I knew what you're actually trying to say and just wanted to spite you because you said it badly.
>>16974725>phenomenait's just geometry, dude
