What's the probability of R in C?

In summary, the conversation discusses the probability of finding the set of real numbers (R) in the set of complex numbers (C). It is determined that there is no way to assign a measure to this event, making the probability of finding R in C equal to zero. The concept of 0+ is brought up, but it is ultimately concluded that it is not a valid real number. The conversation ends with the closure of the thread due to the original poster's refusal to listen to other perspectives.
  • #1
Sabine
43
0
R ]-∞;+∞[ Є C (complex numbers) so what's the probability to find R in C?

i think it is barely equal to more 0+
 
Physics news on Phys.org
  • #2
The probability of finding R in C is equal to the probability of finding 5.29 in R (or any number, for that matter). Infinitessimal (actually, transfinitessimal :P)
 
  • #3
In order to define probability you need to assign a measure to the sets in the sample space. There isn't really a way to do that for R in C, but by any reasonable measure (ie not a probability one) then the measure of R in C is zero.
 
  • #4
i've been thinking of it and i think it's indetermend
 
  • #5
Well, it's not defined, that's different.

You need (*you*) what you mean by "picking a number at random" or "finding R in C".

If we take the set of complex numbers of modulus at most K, then the probabilty that a number selected uniformly at random will be real with probabilty 0 since the lesbegue measurable sets are the "events", and the reals have measure 0 in that set.
 
  • #6
in that case the probabilty is not 0 it is 0+ bcz this number may be found (sorry for my vocab i am french educated)
 
  • #7
What on Earth is 0+? is that even a real number? Don't think it's one I've heard of.

Given any lebesgue measurable subset of C with finite measure, eg the disc of radius K, there is a probability measure on it. If u is lebesgue measure, and T is the measure of the set, then u/T is a probability measure, and the events we can describe are what is the probability that a number picked at random is in S where S is a lebesge measurable subset is u(S)/T

Since the strictly real numbers will form a set of measure zero, the probability of picking a real from this set is zero. Not zero+ whatever that may be.

This is a consequence of how we *define* probability for such discussions.
 
  • #8
0+ is the number that comes right after the 0 (0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000...1) it is the smallest number after zero
 
  • #9
Right, ok, doesn't the fact that there is no such thing as "smallest nonzero positive real number" bother you? after all( 0+)/2 is another number, bigger than zero and smaller than the one you just wrote, which, by the way, isn't a real number, or at least isnt' a decimal expansion of any real number.
 
  • #10
The fact that it's possible for an event to occur does not imply that the probability of that event occurring is greater than zero.
 
  • #11
but the occurence of this event is barely negligeable compering with the universe in which i am studying the probability .

for the 0+ this is its definition that's why i can't give u the exact number but u can find the 0+ maths books so i don't understand why u are discussing it it is a FACT it is universally known.
 
  • #12
Sabine, I assure the notion that there is a real number "just greater than 0" (ie bigeer than zero but smaller than any other real number) is not a sound one.
 
  • #13
Thread closed. Not only is it in the wrong place (this is not a number theoretic issue), but the original poster seems to be more interested in preaching than listening.
 

1. What does "R in C" mean in terms of probability?

"R in C" refers to the likelihood of an event, outcome, or value (represented by the letter R) occurring within a set of possible outcomes or sample space (represented by the letter C). In other words, it is the chance that a specific result will happen out of all possible outcomes.

2. How do you calculate the probability of R in C?

The probability of R in C can be calculated by dividing the number of favorable outcomes (outcomes that satisfy the condition of R) by the total number of possible outcomes in the sample space (represented by C), and expressing the result as a fraction, decimal, or percentage. This is known as the classical or theoretical probability.

3. What is the difference between theoretical and experimental probability?

Theoretical probability is based on the assumption that all outcomes in the sample space are equally likely to occur, while experimental probability is based on actual observed data from experiments or trials. Theoretical probability is used to predict outcomes, while experimental probability is used to analyze and interpret data.

4. Can the probability of R in C be greater than 1 or less than 0?

No, the probability of R in C is always between 0 and 1, inclusive. A probability of 0 means the event is impossible, while a probability of 1 means the event is certain to occur. Any value outside of this range would not make sense in terms of likelihood.

5. How does the sample size affect the probability of R in C?

The larger the sample size, the more accurate the probability of R in C will be. As the sample size increases, the experimental probability will approach the theoretical probability. This is because a larger sample size provides more data points and a better representation of the entire sample space, reducing the influence of chance variations in the data.

Similar threads

  • Linear and Abstract Algebra
Replies
1
Views
901
  • Linear and Abstract Algebra
Replies
1
Views
456
  • Linear and Abstract Algebra
Replies
1
Views
760
  • Linear and Abstract Algebra
Replies
15
Views
976
  • Linear and Abstract Algebra
Replies
15
Views
975
Replies
6
Views
2K
  • Linear and Abstract Algebra
Replies
17
Views
1K
  • Linear and Abstract Algebra
Replies
1
Views
877
  • Linear and Abstract Algebra
Replies
2
Views
731
Replies
5
Views
1K
Back
Top