Say you pick two random straight lines in 3 dimensional euclidean space, what's the probability that they intersect?

Say you pick two random straight lines in 3 dimensional euclidean space, what's the probability that they intersect?

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en.m.wikipedia.org/wiki/Almost_surely
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0%

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

/thread

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

an uncountably infinite number of times

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

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

>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.

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?

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.

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.

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%

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]

gtfo

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

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.

>0%

This.

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

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

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

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

>He still believes the universe uses wraparound scrolling

>all infinities are equal

my head is break

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.

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

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.

>physics

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

Infinite

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

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.

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

∞/∞ = 1
1/∞ = 0
1 = 0

...

They will almost surely not intersect.

en.m.wikipedia.org/wiki/Almost_surely

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

Oh shit

H-h-h-hivemind

...

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

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

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

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.

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?

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

It's being played in reverse.

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.

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

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.

wrong , retard

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.

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?

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

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

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.

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

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

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

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

VSauce said that's possible!!!

>∞/∞ = 1

What's wrong about it?

∞ is not a number.

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

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.

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.

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

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?

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

There is no void.

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

I know that.

Where does my genious equation imply that?

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

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

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

see

>derp

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

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.

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

Yes, but not in reality.

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.

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

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

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

looks like you don't understand

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.