Prove that the Probability of the Impossible Event is Zero

Prove that the Probability of the Impossible Event is Zero

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[larspos]

Isnt it possible to prove the statement without using axiom 2? Once we find P(S)=P(S)+P(⍉), it directly folows P(⍉)=0 (you do'nt even have to use S, any set works).

[coolHarry]

Love your work. Helps me keep going with my learning :) Thanks the recent splurge in proof math it’s really been lifting my interest in different areas.

[bakirnahi]

Just beautiful!! It is a nice feeling of gratitude when after a time to understand the proofs in math you get also in love with math!

[SimoExMachina]

In Finland we use the notation m.o.t. (= "mikä on todistettavaa") as a sign of finishing a proof, which is the same as the latin q.e.d. (quod erat demonstrandum). Alternatively we may use a small empty box (without the cross).

[ricardolopes]

I was thinking if you shouldn't prove before that the axiom 3 is also true for finite sequences of disjoint sets

[KeyserTheRedBeard]

stunning video The Math Sorcerer. I crushed the thumbs up on your video. Maintain up the outstanding work.

[johannesvaasalainen]

Hi! I think there is a problem in this proof if we are very careful. Axiom three doesn't say that you can count the probability of P(A U B)=P(A)+P(B) even if A and B are mutually exclusive. Axiom three talks about infinite sequence of events... You can proof of cause that P(A U B)=P(A)+P(B) is indeed true, but it does not follow directly from axiom three.

[shunsukenatsusawa]

Intuitively obvious, but the proof is an another problem, isn't it? Meanwhile I'm enjoying a cup of cardamom coffee now, just a smidgen cardamom into coffee, then you can experience the depth of flavor of coffee ! Please try it.

[heyman]

why mathematicians ate like that!!!!
The probability for an impossible event to happen is zero, I think it is an axiom

[robertnyc]

Probability is the branch of math I dislike the most. I passed the one obligatory course in second time, I was only 1 point above the corner :) unfortunately 100% of job orders related with Mathematics are Probability, Statistics and its applications (Finance, Data analysis, machine learning) so its not easy for me to find a Job.

[igorkarlic]

Just another observation: Sample space is defined as (wikipedia):

"In probability theory, sample space (also called sample description space[1] or possibility space[2]) of an experiment or random trial is the set of all possible outcomes or results of that experiment.[3]"

But impossible event (outcome) CAN'T be the member of this set! It it were it would be possible. This is a paradox. So axiom 2 fails here. I think Wittgenstein would agree the words are not defined according Logical positivism norm. LOL

REGARDS

[خالدالحماديالحمادي-به]

Nice proof and Thanks for your efforts I wonder if you can make a video in your opinion what is the most Efficient way to read a maths book.

[balachandar]

But sir empty set fi is a subset of every set so how S and fi are mutually independent ? pls answer sir

[Cataclism]

What I don't get is why would we even need to prove such an obvious thing. This is basically an axiom right?

[mlTS]

Nice
OR we can use m/n
m is no of favourable outcomes which is equal to zero
n is total no of possible outcomes
required probability = 0/n=0

[alijattjatt]

sir i want to contact you, can i get your email ?