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Author Topic: Things that made you RRRRRRAAAAGGGGEEEE today: Trust-o-nomics Edition  (Read 2801299 times)

Spehss _

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Re: Things that made you RRRRRRAAAAGGGGEEEE today: FLUSH THAT SHIT Edition
« Reply #49455 on: January 21, 2015, 09:01:12 pm »

.(0)1 is not a real number because you cannot have an infinite number of zeroes, ended by a 1.
Ok, but... what exactly is the logic behind that bit?
Because by having infinite zeros before 1, you never reach a stopping place to put the one. There's always more zeros to add to the end, because it's infinite.

...that's my logical reasoning behind that, at least. Cannot confirm, because I am not Vector. Vector is now a mathematical ninja. Also I don't know what I'm talking about.
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Tawa

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Re: Things that made you RRRRRRAAAAGGGGEEEE today: FLUSH THAT SHIT Edition
« Reply #49456 on: January 21, 2015, 09:02:54 pm »

.(0)1 is not a real number because you cannot have an infinite number of zeroes, ended by a 1.
Ok, but... what exactly is the logic behind that bit?

Because in this case, the infinite we assume that we're talking about--by definition--is the countable kind of infinite we were all talking about earlier. So, it's not like "no, you inherently cannot have infinite zeroes and then a one," but rather "we define the real numbers to act in such and such a way because they have certain nice properties."
Alright then.
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MagmaMcFry

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Re: Things that made you RRRRRRAAAAGGGGEEEE today: FLUSH THAT SHIT Edition
« Reply #49457 on: January 21, 2015, 09:18:25 pm »

Okay, here's an actual explanation of why 0.999... = 1 (at least in the real numbers):

Real numbers can be formally defined as the completion of the rational numbers, which can for example be constructed by dividing the ring of rational Cauchy sequences by its maximal ideal of rational null sequences. Bit technical, but I'll try to explain using common words.

A rational Cauchy sequence is basically any sequence of rational numbers which you can make arbitrarily narrow just by cutting off enough of the start of the sequence. To define the real numbers, every rational Cauchy sequence shall represent (i.e. converge to) a real number. Now we declare that two Cauchy sequences converge to the same real number if and only if the sequences' difference converges to 0.

For example the rational sequence (1, 1, 1, 1, ...) is Cauchy, since it already has no extent and is arbitrarily narrow even without cutting anything off. The rational sequence (0, 0.9, 0.99, 0.999, 0.9999, ...) is also Cauchy, since removing the first n elements makes it 10-n wide, which can be arbitrarily small for sufficiently large n. Now the difference (1, 0.1, 0.01, 0.001, 0.0001, ...) of these sequences becomes arbitrarily close to 0, so these sequences converge to the same real number.

Now by definition of real decimal representations, the real number corresponding to a decimal representation is defined as the limit of the sequence of rationals obtained by cutting off the representation's tail later and later, e.g. 3.14159... is defined as the limit of the rational Cauchy sequence (3, 3.1, 3.14, 3.141, ...). To answer the question of whether 0.99999... = 1, we just look at the example above, and see that they must represent the same real number.
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Vector

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NullForceOmega

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Re: Things that made you RRRRRRAAAAGGGGEEEE today: Decimals of Wrath Edition
« Reply #49459 on: January 21, 2015, 09:30:44 pm »

And here's my take, "Your model is inherently flawed."
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Putnam

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Re: Things that made you RRRRRRAAAAGGGGEEEE today: Decimals of Wrath Edition
« Reply #49460 on: January 21, 2015, 09:37:02 pm »

And here's my take, "Your model is inherently flawed."

You have to be pretty arrogant to think that you know better than the entire body of mathematicians for the past hundred years.

ggamer

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Re: Things that made you RRRRRRAAAAGGGGEEEE today: Decimals of Wrath Edition
« Reply #49461 on: January 21, 2015, 09:44:17 pm »

I have yet to encounter a profession where the difference between .999 to the trillionth place and 1 was at all critical.

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Re: Things that made you RRRRRRAAAAGGGGEEEE today: Decimals of Wrath Edition
« Reply #49462 on: January 21, 2015, 09:47:43 pm »

It's not, and this is to the infinitieth place. Infinitieth is not a word, nor is it a thing, so it's not a distinction at all at that point. >:(

Vector

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Re: Things that made you RRRRRRAAAAGGGGEEEE today: Decimals of Wrath Edition
« Reply #49463 on: January 21, 2015, 09:51:44 pm »

I have yet to encounter a profession where the difference between .999 to the trillionth place and 1 was at all critical.

welcome to pure mathematics \o/
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ggamer

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Re: Things that made you RRRRRRAAAAGGGGEEEE today: Decimals of Wrath Edition
« Reply #49464 on: January 21, 2015, 09:55:01 pm »

Assume that Achilles has to walk half the distance to his ship to reach his ship. If he can only walk half the distance, fuck you your system is flawed this is mathematics m8 com at me u hear keep gaffin bout tha mouf i'll set u roit up m8 try me ill kut u m8 il fukin do it

Tawa

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Re: Things that made you RRRRRRAAAAGGGGEEEE today: Decimals of Wrath Edition
« Reply #49465 on: January 21, 2015, 09:56:03 pm »

...What the hell was that?
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ggamer

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Re: Things that made you RRRRRRAAAAGGGGEEEE today: Decimals of Wrath Edition
« Reply #49466 on: January 21, 2015, 10:09:07 pm »

a half remembered version of one of zeno's paradoxes combined with me being an asshat

i'm not very good at the whole humour through text thing

hops

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Re: Things that made you RRRRRRAAAAGGGGEEEE today: Decimals of Wrath Edition
« Reply #49467 on: January 21, 2015, 10:19:21 pm »

I have yet to encounter a profession where the difference between .999 to the trillionth place and 1 was at all critical.
It's actually basically the fundament of calculus if I understand it correctly.

0.999... recurring being equal 1 means that if a + 1 = b, then a + 0.999... = b, which is why you can say that when a number seems to be approaching a certain number, but doesn't quite seem to reach it, you can still say that the limit approaching that number is that number.

This also answers Zeno's Paradox because the distance between Achilles and the turtle decays to 0.000...1 which is equal to 0, so it means that at t = ∞ Achilles will reach the turtle.

It's also the reason why bullets and pretty much all motions in the universe can actually happen instead of the universe glitching out.
« Last Edit: January 21, 2015, 10:21:03 pm by Objective »
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NullForceOmega

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Re: Things that made you RRRRRRAAAAGGGGEEEE today: Decimals of Wrath Edition
« Reply #49468 on: January 21, 2015, 10:25:58 pm »

No really, mathematics is simply a model based on our perception, and our perception is imperfect.  Ergo, your model is flawed.  I never claimed to have a better answer, but anyone who's even bothered to look at the model should fully comprehend that it is inherently flawed.
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hops

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Re: Things that made you RRRRRRAAAAGGGGEEEE today: Decimals of Wrath Edition
« Reply #49469 on: January 21, 2015, 10:28:06 pm »

What model? Do you mean the Achilles thing or the fact that 0.999... = 1?
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