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
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.
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.
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?)
>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
>I meant real like the set...and imaginary like iota ones
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
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
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.
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.