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how would you explain to someone with little...
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You are currently reading a thread in /sci/ - Science & Math

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how would you explain to someone with little math knowledge that the probability of picking a particular real number between 0 and 1 is exactly 0 and not "infinitely small" ?

the latter kinda make sense in real life, i guess
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>>7804865
Well, infinitely small has no meaning, in the first place.
Ask them to construct an infinitely small number, and if they say "0.0000.....1" then explain to them that the number they constructed cannot exist, since it's paradoxical-
Either it terminates in 1 after a finite number of 0's, or it's infinitely many 0's; it cannot be both.
>>
Number of digits after decimal point of any given real number is infinite. Probability of being able to enumerate infinite number of digits = 0. QED.
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>>7804865
The hang-up here is that the only number than can fit any reasonable definition of "infinitely small" magnitude is zero.

If infinitely small is taken to be "smaller than any positive real number", then it's obvious it can't be positive since else you could take the average of it and zero.
>>
(op here)
yeah i tried something like that but then they told me that the probability would not be a number

what i'm asking for is a reason that "physically" makes sense, if possible. the argument "it cannot be another number so it has to be 0" isn't very satisfying

(also general pedagogy thread, i guess?)
>>
ok I'm probably making a fool of myself but...
aren't all numbers except imaginary ones real? so, shouldn't the probability be 1
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>>7804894
go back to your containment board pls
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>>7804892
>yeah i tried something like that but then they told me that the probability would not be a number
then you can't explain anything to them if they refuse to accept how babby tier probability is defined
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>>7804894
They are talking about selecting a specific number. Like, for example, selecting EXACTLY
.11010105010501494951 from the set of real numbers [0,1]
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>>7804894

wut

imaginary numbers are as real as "real numbers"
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>>7804936
>>7804936
... They're not included in the set of Real numbers.
[math]
\mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R} \subset \mathbb{C}
[/math]
>>
>>7804907
Thanks
>>7804936
I meant real like the set...and imaginary like iota ones
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>>7804957
>I meant real like the set...and imaginary like iota ones
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>>7804970
Imaginary=Complex number
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>>7804865
Well you should say that numbers such as 1,2,3,4.... Are known as countable infinity
While numbers between numbers such as 0 and 1 are called uncountable infinity because there are literally infinite combinations to choose from
You can explain like this
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>>7804865
Math retard here. A real number is anything that exists on a number line, right? So for instance, every number in the infinite set between 0 and 1 is real. Therefore, wouldn't the probability be 1? Since you could literally pick any number greater than zero and less than one and find it on the line?

pls no bully
>>
>>7805071
see >>7804907
>>
>>7805071
Ah I see. Thanks. Is that because no such terminating number exists, and there will always be another decimal place? I was assuming that real numbers meant that it was terminating and occupied a specific, fixed place on the number line and could therefore be selected.
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>>7805160
of course it can be selected, but the probability of selecting it at random is 0
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>>7805160
Irrational (never ending) numbers, like surds are real
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>>7805165
Ahhhh selecting it at random. It's clicked. Thanks anon.
>>
The probability that you choose a specific random number between 0 and 1 is equal to the inverse of however many decimal places you want to go.
In other words, take 'x' to be the number of decimal places you want to go.

As 'x' approaches infinity, the probability of choosing a specific number becomes 1/x.
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