Say you pick two random straight lines in 3 dimensional euclidean

>>8342638
0%

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I got to answer with the classic: 50%. Either they intersect or then they don't.

>>8342641
/thread

>>8342641
Okay so how many times do you have to pick a random line before the probability of any two of them intersecting is nonzero?

>>8342645
an uncountably infinite number of times

>>8342641
But doesn't that imply that intersecting straight lines in 3d euclidean space are impossible?

>>8342653
through random means yes.
are you implying choice is the same thing as random occurrence?

>>8342655
>through random means yes.
That can only be true if random selection automatically exclude intersecting lines, which, being random, it shouldn't.
Also more pertinently, doesn't this imply that 1/infinity = 0? This can't be right either.

>>8342661
If you think [math] \frac{1}{\infty} \neq 0 [/math], why dont' you go through a mathematical proof to try and find a number smaller than [math] \frac{1}{\infty} [/math]

the only lines that intersect are the ones that share a planar cross section of 3D space. Can you tell me how many planar cross sections there are in 3D space, and what is the liklihood of selecting just one?

>>8342670
But since it's a random selection it -must- be capable of choosing intersecting lines (since intersecting lines are in the set of possible choices), which implies the probability has to be nonzero.

>>8342677
but the probability of selecting two intersecting lines is [math] \frac{1}{\infty} = 0 [/math]

We're working within a purely mathematical construct here. it doesn't have to obey your notions of common sense.

if you want, you can define a number smaller than any other number and have that be the value.

>>8342693
Maybe my quandary would make more sense phrased a different way.

Say you choose a random point from within [0,1] to remove from the set. You're saying the probability of picking any individual point would be 0%. But this is impossible since the individual probabilities must sum to 1, and even uncountably infinite * 0% = 0%

>>8342693

Oh I can find a number smaller than (watch me fuck up) [math]\frac{1}{\infty}[/math] alright
How about [math]\frac{1}{\infty}^{2}[/math]

>>8342642
gtfo

>>8342709

that would imply that [math] \infty^2 > \infty [/math] which is silly (and a contradiction)

>>8342702
you can't pick every number in the interval [0,1] one at a time, hence un'countable'y infinite.

you would have to pick ranges of numbers or open subsets, but then you would be picking infinitely many numbers at once.

Since the lines are infinitely long and infinitely thin, the chance is infinitesimally small.

>>8342641
>0%

This.

>>8342793
I'm not saying pick all of them, just one, at random.

Oh shit infinity has undefined cardinality! When did that happen.

1/blue=wtf is maths

so I'd contend that because it's within possibility for the lines to intersect there's no way that 0 and 1/∞ can be the same

there are infinity choices

therefore the chance is 1/infiniity

imagine you have a giant swimming pool of jelly

and you shoot small bullets at it, and they leave a trace

what are the odds shooting randomly, their paths intercept each other?

that's your question, except the swimming pool is infinitely big

>>8342661
Learn some measure theory and proper probability theory. Inhabited sets can have zero measure.

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100%

why?

>lines are infinitely long
>space is an infinite number of points
>an infinite number of points is a sphere at all points
>spheres are curved

so the lines will intersect infinitely. that's why they say space is curved

The probability is an unbounded number approaching 0%

You have to different infinites:

A) an infinite amount of pairs of lines that intersect each other
B) an infinite amount of pairs of lines that do not intersect each other

B is obviously more dense than A even though both are infinite. If you invent a number to measure the density of infinite sets, say 'a' and 'b'

The odds are a/b

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>>8344236
So in other words its 50%, it either doesnt or it happens?

>>8344233
>He still believes the universe uses wraparound scrolling

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>>8344233
>all infinities are equal

>>8344236
my head is break

>>8344243
kek

the universe is curved because of conservation of energy

if you shoot a photon into space and it doesnt collide and instead travels into the "void" beyond the universe, that energy is lost forever.

>>8344262
the energy still exists even if it's hella far away from any matter

>>8344267
No, that's wrong.

There arent any strings in the void, and thus matter can't exist where strings do not exist, since strings give matter form.

Read more about M please.

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>>8344273
>physics

>>8342638
placing a line (1d) on a 3d space
is equivalent (for this purpose) to
placing a point (0d) in an infinte 2d space

thus, the question can be translated to
given an infinite 2d sheet
what's the probability that you would pick the exact same place twice in a row?
that probability is (1/infinity)^2 = 0

>>8342638
Infinite

>>8342646
Probability measures are only defined for countable unions, so I think you'll have trouble actually defining that

>>8344163

Fucking normies. The other guy has spelled it out for you many times. Is this going to take a coloring book?

This is an infinitesimal. It isn't real-valued. It approaches 0 as the number of planar cross-sections in the space approaches infinity. Which they do.

Insisting that the answer must make sense to you doesn't change the answer.

>>8344219
A line has no volume.
Something that has no volume, can not intersect with something that has no volume.
It can only be 0.

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∞/∞ = 1
1/∞ = 0
1 = 0

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>>8344468

>>8342638
They will almost surely not intersect.

https://en.m.wikipedia.org/wiki/Almost_surely

Correct answer: the probability is *almost surely* 0.

>>8344471
>>8344472
>>8344473

Oh shit

H-h-h-hivemind

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>>8344468

>>8342638
lol they have to be perfectly parallel. even the smallest shift from parallel means intersection.

according to the laws of probability, there is a difference between something surely happening and something almost surely happening

therefore there is a difference between 1 and 1- 1/infinity
therefore there is a difference between 1 and 0.999recurring

checkmate

>>8344502
we are talking about 3d euclidean space, not 2d space.

finite line segments, infinite lines or rays?
how dou you pick them, chosing two points on a line, or a point and an angle or some other way?

If you narrow down your question you already have the solution

>>8344505
Why is 1 not equal to 1- 1/infinity?
is 1/infinity not equal to 0?
please elaborate.

>>8344518
1/infinity is equal to a/b

where a is the size of the set of lines that are parallel to a particular line in R^3 and b is the size of the set of straight lines that can exist in R^3.

>>8344276
I wonder how these things are generated.
Do they pick some stable final construct and generate every possible leading set, and expand out like that, or is there some sort of black magic easier method?

>>8344525
I don't see the logic.
both a and b equals to infinity

>>8344529
It's being played in reverse.

>>8344536
but the bottom infinity an order of infinity higher, making it cancel out and be equivalent to 1/ infinity

and since by the laws of probability there is a difference between surely not almost surely not there must also be a difference between 0 and 1/infinity.

and so there must also be a differnce between 1-0 and 1-1/infinity and thus 1 =/= 0.999 recurring

You cannot allow for surely =/= almost surely without allowing this.

>>8344714
But how can they meet, when they have no volume?
That would be impossible, right?

>>8344740
how can what meet ?

how can lines in 3d meet?

are you saying that the point 0, 0, 0 is not part of both the x axis and the y axis at the same time?

Answer: it's impossible to choose an element of an infinite set randomly.

>>8344747
wrong , retard

>>8344744

Oh. Yeah I see what you mean now.
You are right.

Though it could never happen in reality, which was what I was thinking about. It could only happen in a fixed system residing in the imagination like euclidian space.
Euclidean space has no place in reality, as nothing can be pinpointed, because everything goes into infinity.

If the lines are infinitely fine, or if there is an infinite amount of space. Then the lines can never meet in reality.

Say you have any line 1. The chance that line 2 is at any particular position is 0, but it still has to be somewhere. So it theoretically could be intersecting with line 1, its not that it cant happen, it just has 0 chance of happening.

>>8344831
not 0, almost zero

the fact that by the laws of probability , 0 =/= almost 0 means that 0 =/= 1/infinity
which means that 1-0 =/= 1-1/infinity
and thus
1 =/= 0.999999...

literally prove me wrong.

picking out the line a line that happens to be perpendicular out of all the possible lines that can exist in r^3 is equivalent to an event with probability 1/infinity

no?

>>8344236
Unfortunately all Euclidian spaces have the same cardinality, from the number line n=1 to infinite spacial dimensions.

>>8344757
true, retard.
show me how to pick an integer randomly or btfo

>>8344916
If 1 doesn't equal 0.99999999, you're violating the Proposition that we can always find irrationals and rationals between any two distinct reals.

>>8345010
Ok fine. Just divide up the normal distribution between the integers so you get an equivalent probability mass function

Or the symmetric exponential distribution.

Or any distribution you want where the support is the integers.

Here's the hint, retard.
Random doesn't mean "uniform distribution"

fucking loser

>>8345014
And if almost surely = surely them you're violating the laws of probability.

If yogic you want to prove me wrong then you need to explain how
>picking out the line a line that happens to be perpendicular out of all the possible lines that can exist in r^3 is equivalent to an event with probability 1/infinity

Is wrong

>>8345010
pic real x in (0;1]
integer is |1/x|
what do I win?

>>8344825
the way you're defining it, lines don't exist in reality so I don't understand why you're still posting shit like "lines can't intersect in reality because they have no volume." Math=/=reality

>>8342790
VSauce said that's possible!!!

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>>8344468
>∞/∞ = 1

>>8345263
What's wrong about it?

>>8345272
∞ is not a number.

>>8345274

according to which definition?
I just used google's:
Infinity:
[Mathematics]
a number greater than any assignable quantity or countable number (symbol ∞).

>>8344163
You're approaching this rationally, so I'll explain it rationally.

Most people who know nothing about math would agree that 1.9999999998 and 1.9999999999 are essentially the same number. Well, 0 and the probability that two random lines in an infinite 3d space will intersect are infinitely closer to one another than the previous example.

Ergo, the probability can be said to be 0, and in fact the only useful way to describe it is that it approaches 0.

>>8345297
Infinity is a *value in theory, it's just not arithmetic. You can't properly divide or multiply something by infinity. It represents an idea of a number that exists in theory, but it isn't a number in the same way that 45 or 5 - 3i are numbers.

>>8345297
infinity/infinity is indeterminate, it can actually equal anything.

heres some examples:

lim 2x + 1/x + 3 = 2
x-> inf


lim x/x^2+ 9 = 0
x-> inf

yeah basically get fucking wrecked. you need to use limits when talking about infinity

>>8345305
I'm sorry, I don't get it.
why is it not a number.
If it has an unknown amount, then you could say that amount is (a), so
a/a = 1
is that not basic math?
have I misunderstood something?

>>8345336

I'm sorry, I don't get it.
see: >>8345378

>>8344273
There is no void.

>>8345272
[math]\frac{1+1+1+1+...}{2+2+2+2+...}[/math] isn't equal to 1 you moron.

>>8345408
I know that.

Where does my genious equation imply that?

>>8345436
You are aware that both the numerator and the denominator in >>8345408 are equal to infinity, right?

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>>8345444
Well I guess we ran into a problem there.
Now it seems that
Infinity =/= Infinity
- That can not be.
If we break it down then 2 =1+1
so it would technically be
1+1+1+1+.../1+1+1+1+... = 1
as with any number
problem solved.

∞ = 0

>>8345472
But then again, you would be able to say that the 1 and the 2 are two different qualities.
so you could say that there is quality a and b:
a/b =/= 1

84.3

>>8345528
see
>>8344468

>>8344445
>derp

so why are there probability measures on [math]\mathbb R[/math], an uncountable set?

>>8345030
You don't know anything because you're uneducated. People like you should stop shitting up this bored with your "prove me wrong" attitude and start being grateful for help.

>>8344454
Erm, what? Lines intersect all the time don't they?

>>8345958
Yes, but not in reality.

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robotic engineering is the future, and most agree the future is now. Don't believe me, just check out the raspberry pi motherboard and feed your algorithms.

>>8345472
this is fucking stupid because you're saying that 1 = 1/2

>>8344243
One day, they'll write in history books about how people thought the universe was flat.

>>8345953
great understanding you must have if you aren't even able to explain why it is wrong.

looks like you don't understand

>>8346994
It's a pointless exercise for me. My only motivation would be to explained it out of the kindness of my heart. If you change your attitude to that of a uneducated student receiving free tutoring(which is what you are) and ask nicely I would be willing to help. Otherwise I won't reply again.

>>8342638
Say you pick two random natural numbers what's the probability that they are the same?

answer: -1/12

>>8347076
that can be stated without evidence can be dismissed without evidence.

>>8346976
no im not saying that 1=1/2, I'm saying that infinity=infinity

>>8342642
[math]\# \mathbb{R}^n = \# \mathbb{R} ^m [/math] for any natural n, m so it's actually 50%

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>>8344233
>100%

>>8344502
you need planes for that in 3d

>>8345472
but the divisor becomes (1+1)+(1+1)+(1+1)+(1+1)... = 1+1+1+1+1+1+1+1... not 1+1+1+1...
so 2* (1+1+1+1...) so whole thing is 1*inf / 2*inf = 1/2

>>8342641
DID SOMEBODY FORGET ABOUT THICC LINES?

>>8342638
In space, a pair of lines can:

>Intersect
>Be parallel (not touch each other and also be contained in a single plane)
>Not touch but also not be contained in a single plane

There is no valid argument to say that one is more likely than the other so everytime you pick two random lines, they will have to fall under 1 of the 3 categories.

Therefore the chance is 1/3

>>8347696
Ok.
I agree.
So this still means that Infinity/infinity=1
This was my starting point.

>>8345536
He said uncountable unions, not uncountable sets.

>>8347709
but my infinities are the same infinities, yours are different infinities, infinity is just a construct for "cant be arsed to figure out the exact uncountably huge number I should put here"

>>8347752
Don't you know that some infinitives are bigger than other infinitives?

*sips starbucks coffee

>>8347752
>but my infinities are the same infinities, yours are different infinities
So you argue that Infinity=/=Infinity ?
How can that be ?

>infinity is just a construct for "cant be arsed to figure out the exact uncountably huge number I should put here"
So what is the proper term to use for something that continues forever if not infinity?

>>8345336
>lim 2x + 1/x + 3 = 2
>x-> inf

>lim x/x^2+ 9 = 0
>x-> inf

Wait what? The first limit is infinite, the second is 9. Am I missing something here?

>>8347709
The expression [math]\frac{\infty}{\infty}[/math] is invalid. Arithmetic operations are not defined on [math]\infty[/math].

>>8347709
I am offended by this

>>8347783
No you are correct, >>8345336 is not thinking straight.

>>8347775
>>8347755
lol but as you can see on that example, its true, just because mathematicians cant be arsed to define it better... I see why though, its infinite and they aren't gonna calculate it anyway, so a single symbol does good enough

think about it being a programming variable or a function, whatever, except you use the same symbol for all of them, thats why inf/inf is undefined, because you may or may not be dividing different values.

without using the infinity symbol:
define a = 1+1+1+1...
then 1+1+1+1.../2+2+2+2... = a/2a = 1/2
then 991346494313646..../1+1+1+1... = b/a = ?, where b = 991346494313646... because it sure as hell ain't a

>>8342641
And if distance between adjacent points is infinity?

The probability of intersection tends to zero. It is NOT equal to 0.

>>8347798
>>8347807
I sort of get how it works now. but then again I sort of don't get it.
still not quite sure what the difference is between what I call infinity and you call infinity.
My definition is something that continues forever.
and what I get from you is that it is something very big, but not quite infinite in the sense that I define it.

>>8347847
it has a ... it goes infinitely, but it has to be a value if you want to use it for any practical reasons.

Your definition gives you greatest number, but as the numbers grow infinitely you can never give it a hard value to it, as there is always an inf+1 that is greater, so inf is actually undefined/only partially defined (because there is no final number). Because it is an undefined infinitely big value you cant use most of arithmetic on it.

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>>8347973
>but as the numbers grow infinitely you can never give it a hard value to it
That clicked
Thanks Anon!

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>>8348423
>but as the numbers grow infinitely you can never give it a hard value to it
Does that mean (pi) has no hard value?
It grows into infinite precision.

>>8342638
Suppose you have a random 2x3 matrix, and a random 2x1 matrix. What is the probability that there exists a 3x1 such that the product of it and the 2x3 matrix is the 2x1 matrix?

>>8342702
infinity*0 is indeterminate, it could be 0, it could be infinity, or it could be 1, or 2, or 100, or whatever. You can deal with these indeterminate cases by studying limits, and learning calculus, or you can become king autismo and learn about hyperreals.

>>8348605
>hyperreals
I like hyperreals.

>>8348605
call it an indeterminate. not infinity.

>>8342670
[math]\tfrac{1}{∞ + 1}[/math]

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>>8349370
You can't do that!!
Because some people don't like if you use ∞!!!