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/sci/ - Science & Math

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9697965 No.9697965 [Reply] [Original]

Suppose a completely random real number were chosen from an uncountable infinite set such as the range [0,1]
What are the chances that this number is exactly 0.5?
It can't be zero, but it is infinitesimally small.
How would this be expressed mathematically?

>> No.9697972

>>9697965
0

>> No.9697974

>>9697972
The chance can't be zero though because it's possible .5 can be chosen

>> No.9697978

>>9697974
Probability theory is based on measure theory, and the measure of a singleton is 0.

>> No.9697979

>>9697972
But using this logic, assuming each number had an equal chance to be picked, this implies that every number in the set is impossible to be picked

>> No.9697984

>>9697974
>it's possible .5 can be chosen

Prove it. Intuition goes out the window when you're dealing with infinity.

>> No.9697985

>>9697965
define "random"

>> No.9697987

>>9697984
>Prove it
Supposing each number has equal probability of being chosen, then the first pick of a random number proves that .5 can be chosen and it is not impossible to pick that number

>> No.9697988

>>9697979
I'll turn this question around. Assuming each number has the same chance of being picked, what's that probability, considering there's an infinite number of them? 1 / infinity ?

>> No.9697993

>>9697984
Forget about .5. Let a number generated from unif[0,1] be x. The probability of it being chosen is 0, but it's clearly possible for it to be chosen.

>> No.9697997

It's zero.

Think of it like this, your answer is always going to be:

0.xxxxxxxx...

Where each x is a random number between 1 and 9.

You can't roll a dice an infinite number of times and get the same number every single time, 0.5000000... isn't a possibility.

>> No.9697998

>>9697988
>what's that probability
the probability clearly is not zero but it is infinitesimally small

>> No.9698002

>>9697997
*0 and 9

>> No.9698007

>>9697998
No, it's literally 0.

>> No.9698011

>>9698007
Suppose all numbers are equally likely to be picked
The first number picked turns out to be y
Therefore the odds of picking x are non zero

>> No.9698012

>>9697987
You'd have to have infinite trailing zeros though, which is impossible

>> No.9698013

>>9698012
0.5 is literally as likely as any other number, are you saying all of them are impossible?

>> No.9698014

>>9698012
Every number has an infinite number of trailing zeros if you wish to write it that way

>> No.9698017

Can we just use calculus rules and let dc represent in infintesimally small change in chance

>> No.9698018

>>9698011
I disagree, anon, rational numbers need to have recurring decimals.

You're never going to get that if the infinite number of decimals is random number between 0 and 9.

>> No.9698021

>>9698013
The chance of picking any one specific number out of an infinity of them is 0
How would you even check what number you picked anyway? You'd have to check an infinite number of decimal places.

>> No.9698023

>>9697965
Suppose we modified the set so that exactly 50% of it 0.4. We reach this by adding 0.4 between any two numbers that are not 0.4.
How much have my chances decreased of drawing a 0.5?

>> No.9698024

>>9698021
Why do you need to check? The probability x will been chosen is 0. x has been chosen.

>> No.9698030

>>9698021
>How would you even check what number you picked anyway
Irrelevant.
The argument remains that if all numbers were equally likely to be chosen, then the first choice of a number implies that there is a non-zero chance for any number in be the set to be chosen.
Unless if you're arguing that it is mathematically impossible for a random number to be chosen from the set [0,1] in which case I'd like to hear your argument

>> No.9698031

>>9698024
Yeah, sure.

Someone should make a lottery with an infinity of numbers to choose from, with some insane payoff.
Probably illegal though, to protect brainlets like OP.

>> No.9698035

>>9698031
I think it's a reasonable question. Probabilities of 1.1 and 0.5 are both 0. Are they equally likely to be chosen?

>> No.9698036

Obviously higher than nil but this simply can’t be expressed mathematically.

>> No.9698039

>>9698036
It's nil.

>> No.9698041

>>9698035
Well in this case, 1.1 has actual probability of 0 while 0.5 has probability of ((0)) according to these anons

>> No.9698043

>>9698039
By definition of 'probability'. Is there a better one?

>>9698041
0.5 is infinitely more likely than 1.1?

>> No.9698048

Imagine this 'distribution': unif[0,1], if it falls on 0.5, unif[1, 1.1].

>> No.9698049

>>9698043
1.1 lies outside of the set

>> No.9698050

>>9698048
Can you say that 1.05 won't be chosen?

>> No.9698056

>>9698030
Yes, they're all equally likely to be chosen, but there's an infinity of them, so you have to divide your chance by infinity and get exactly 0
see https://www.youtube.com/watch?v=-6HxjiW_KwA

>> No.9698060

>>9697965
>Suppose a completely random real number were chosen from an uncountable infinite set such as the range [0,1]
Can't be done.

>> No.9698066

>>9698056
I agree with everything you said, but if all of their possibilities are exactly zero and it is impossible to have any number chosen
>>9698060
Why

>> No.9698071

>>9697965
the problem is the question itself. You can't ask about probability without specifying probabilistic model. In this case, the distribution. So if the distribution is uniform, the probability is 0. But if we were sampling from measure concentrated in 0.5, the probability would be 1.

>> No.9698309

>>9698056
Think of the implications of this argument mathematically. This argument proves a finite Universe in itself, for if the universe were infinite the chance of us developing life here on Earth would be exactly 0

>> No.9698335

So it is not possible to have a random number chosen between 0 and 1?

>> No.9698350

What's 1/(inf)? 0, of course. Infinitesimals are not real.

>> No.9698356

>>9698350
In calculus they are very real and are called dx

>> No.9698410

>>9698013
Knowing that you randomly selected 0.50000000....... is impossible.

I'm not a math fag but you run into constraints with time in determining you randomly selected a given number, and in generating the list to choose from.

Here's a question, if you can measure an infinite number of decimal places per moment of time, and also generate a list of an infinite amount of numbers between 0 and 1 in a given moment of time, could you randomly selected, and know that you randomly selected a given number?

>> No.9698438

>>9698350
Math is just something we made up. We can say anything we want is real.

In math, if you say it’s real, then it automatically becomes real, exactly just as real as any other kind of math.

>> No.9698442

>>9697974
Zero doesn't mean impossible.

>> No.9698452

>>9698438
Ok, sure, it's just a different way to write 0.

>> No.9698453

>>9698410
Everyone here can see you are retarded as fuck. To explain it to a brainlet like you:

This is like saying pi is rational because “hurr durr no paper in the world is big enough to write down all the digits hurr durr”.

>> No.9698456

>>9698452
In one context it is zero, in a different context it’s a certain infinitesimal.

Both contexts are equally valid, and one can never be more correct than the other.

>> No.9698462

>>9698442
Then what are the chances of it happening, buttbrain?

>> No.9698465

>>9698410
I don't get these comments about time constraints. Can you say anything about the number that got picked? In this >>9698048
case, can you check if it's over 1?

>> No.9698474

The chance is clearly non zero

>> No.9698492

>>9698442
>Zero doesn't mean impossible
Yes, it does.
A zero probability means it will never happen, it is not possible to happen, it is impossible

>> No.9698493

>>9698462
0. What a retarded question.

>>9698492
Wrong. It means it will almost never happen but it's still possible.

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

>> No.9698550

>>9697993
.5 will almost certainly not be chosen

>> No.9698560

>>9697965
Every introduction to statistics class covers this problem. It's 0.

>> No.9698621

>>9698493
>0. What a retarded question.
So you're claiming that the sum of an infinite number of 0 probability events is 1?
In other words if you add 0 an infinite number of times to 0 you get 1?

>> No.9698633

>>9698560
>doesn't read the OP

The OP addresses this. He said it's not zero, learn to read next time.

>> No.9698641

>>9697965
if you want to select .5 from [0,1] and you have a set of 10 numbers then you would have 1/10 chance of getting it right.
if you have infinite set of numbers in the same range then you have 1/inf chance of getting it right
and 1/inf=0

so >>9697974 is right

>> No.9698666

>>9698621
>So you're claiming that the sum of an infinite number of 0 probability events is 1?
Please learn basic mathematics before posting.

>> No.9698674
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9698674

>>9698011
The chance of picking y is still zero.

>> No.9699086

>>9697965
hmmm...
one possibility out of infinite possibilities

1/infinity = 0

>> No.9699215
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9699215

>>9697965
>uncountable
>infinite
>SET

>> No.9700173

>>9698335
Sure, but you need a restriction like all numbers between 0 and 1 with less than X decimal places.


Where X can't be infinity.

>> No.9700185

>>9697965
If it's uncountable, you can't randomly choose a number. It's not zero, it's error.

>> No.9700212

>>9698621
>So you're claiming that the sum of an infinite number of 0 probability events is 1?
Probability measures do not have uncountable additivity, only countable additivity property. Therefore summing the probabilities of uncountable events says nothing about the measure space.

>> No.9700228

>>9698007
>>9697972
Lear what is a LIMIT, faggot. It is not 0. I would say it is inf^-1

>> No.9700232

>>9697993
>The probability of it being chosen is 0, but it's clearly possible for it to be chosen.
nice oxymoron

>> No.9700588

>>9700232
How do they conflict?

>> No.9701520

>>9697965
If there is no limit to how long the irrational number can be, you can't get a "proper" answer.
But as the length of the irrational number increases, the chance of getting 0.5 exactly approaches 0.

>> No.9701527

>>9700212
You can't sum an uncountable set. + takes a countable number of arguments.

>> No.9702009

>>9697965
Usually probability is represented by the area under the curve of a probability density function, so knowing the probability of an exact value occurring on a continuous distribution is impossible. IIRC probability is usually expressed as P(x< or > X) rather than P(x = X) for this reason

>> No.9702108

>t. don’t know what continuous probability is

>> No.9702308

>>9700228
I know what a limit is, mate, and I'm telling you it's impossible to role a fair 10 sided dice (0 - 9) for each decimal place, an infinite number of times and get 0.500000...

Sorry, but it's zero.

>> No.9702367
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9702367

>hurr durr what is a Borel measure

>> No.9702395

>>9698071
with no further information uniform distribution is implied.

>> No.9702841

>>9700185
>If it's uncountable, you can't randomly choose a number.
Why not?

>> No.9702845

>>9697965
>uncountable
Zero

>> No.9702849
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9702849

>it’s a sophomore can’t into analysis thread

>> No.9702850

You can normalize infinity.

You cannot normalize uncountable infinity.

>> No.9702858

>>9701527
>You can't sum an uncountable set.
You can, you just have to make sure that every countable subset is convergent. The sum of uncountably infinite 0s is 0. But this is irrelevant since probability measures only have countable additivity, meaning only summing countable sets is informative.

>> No.9702922

>>9702858
How do you define the converging series of an uncountable set?

>> No.9703176

>>9702922
There is no guarantee that the series converges, only the countable subsets have to be convergent. The limit of those subsets can be infinite.