Two questions that have nothing to do with programming

[chrisname]

1. How many possible true and false statements do you think there are: finitely many or infinitely many?
2. If S is an infinite set and T is a finite set, given that x belongs to one and only one of them, what is the probability of x belonging to T and not S?

[MiiNiPaa]

2. Depends on how we select x. In general case it is infinitely small number.

[z05DSL3A]

1- None
2- 1:2

[chrisname]

@MiiNiPaa
Assume x is selected at random.

What about question one?

[devonrevenge]

whats that mathematical paradox with the game show host and a 50/50 chance of winning a prize behind the door?
thats not a good description, An expert programming buddy (a python man!!) showed me something that blew my mind, i will find it for you know, I suspect my first paragraph didnt pertain enough cues to boost your memory.

_{grey wolf seems to get it every time i do this}

[z05DSL3A]

Monte Hall’s “Let’s Make a Deal”

[MiiNiPaa]

2.

MiiNiPaa wrote:

In general case it is infinitely small number.

1. As there is finite amount of facts and finite amount of words and ways to combine it, it is finite for both.
EDIT: on second though: you can name still unnamed member of infinite sets and state facts about them. So it is Infinite for both :)

[helios]

True is a true statement. False is a false statement. [EDIT]Two statements can be joined by logical conjunction to make another statement.[/EDIT] Let f(x, n) = foldl(&&, True, [x | _ <- [1..n]]). For all natural values of n, we have that:
1. For all x ∈ {True, False}, f(x, n) is a statement equal to x.
2. f(x, n) == f(y, m) ⇔ x == y && n == m
Thus, for all x ∈ {True, False}, #{f(x, n) | n <- N} == #N.

One might even argue that foldl(&&, True, [True | _ <- [1..]]) is true, but once we get to infinite strings, things get tricky.

[MiiNiPaa]

It is simplier. For each natural number we can make at least one true statement and one false statement. There is infinite number of natural numbers, so there is infinite number of true and false statements.

How many do you think there is statements which aren't true or false?

[devonrevenge]

Grey Wolf wrote:

Monte Hall’s “Let’s Make a Deal”

XD thats the one mr wolf.

a buddy made a program that demonstrated working, i couldn't get my head round it, could you write a program to solve your problem

(do you want a link to the python mony hall program)

[N36fSL3A]

Wait a minute, true is always true. But if you choose false it would be true unless false is equal to true, which would be false but false would equal true. Something being false is a paradox

[devonrevenge]

we shouldnt even try and join in fredbill this one is for grownup mathematicians :P

[N36fSL3A]

oh ok. *opens up his first grade level math book*

[Lachlan Easton]

1. Infinitely many. For any true statement you can apply a negative to make it false. eg "My name is Lachlan" is true "My name is NOT Lachlan" is false. You can then apply a double negative to make it true again "My name is NOT not Lachlan". You can continue to do this recursively.

[firedraco]

1) Infinitely many. In particular, a countably infinite number, I think.
2) 0. (Almost never)

[helios]

2. It depends on the size of U (the set of all possible values of x and nothing else) relative to S and T; and on the probability distribution of x over U. For example, if S = N - {1, ..., 10}, T = {1, ..., 10}, U = N, and the distribution is uniform, you will almost always have that x ∈ S. Keeping everything the same, but letting U = {1, ..., 11}, we have that P(x ∈ S) = 1/11.
Keeping a uniform distribution: U is finite ⇔ P(x ∈ T) > 0.

[tition]

+1 to helios, here is the wikipedia page explaining what is a distribution probability function P:
http://en.wikipedia.org/wiki/Probability_distribution


To 1:
It is not clear to me what you mean by "how many ... there are": is it a philosophical question, or a mathematical one?

If it is a mathematical question: here are infinitely many true statements for you:

(n+1)(n-1)=n^2-1
for any integer n. Since there are infinitely* many integers (by one of the set-theoretic axioms), there are infinitely many true statements.

Note that the existence of natural numbers is an axiom, it does not follow from anything else. It is not self-evident, nor is it known, whether there exist infinite sets in nature. That includes all known aspects of observation and measurement (is time continuous, or is it discrete (split into smallest indivisible units, of which there have been finitely many since the beginning of time, and finitely many more to go))?

*In mathematics, a set is said to be infinite if it has the same cardinality (size) as one of its proper subsets.

[MiiNiPaa]

MiiNiPaa wrote:

2. Depends on how we select x. In general case it is infinitely small number.

chrisname wrote:

@MiiNiPaa
Assume x is selected at random.

A random here is probably means that x ∈ T ⊖ S

[andywestken]

Edit: missed Lachlan Easton's post on first scan...

How many do you think there is statements which aren't true or false? 

Not quite sure whether you mean

"How many of you think there are statements which aren't true or false?"

or

"How many do you think there are, statements which aren't true or false?"

But there must be some sort of infinity of undecidable statements.

Andy

Undecidable problem / Examples of undecidable statements
http://en.wikipedia.org/wiki/Undecidable_problem#Examples_of_undecidable_statements

[BigBlackSheep]

@helios
S is an infinite set.
The chance of x being in T is almost never. You're comparing a finite to an infinite magnitude.