For questions on provability, the capability of being demonstrated or logically proved.
Questions tagged [provability]
258 questions
2
votes
3 answers
Proving that there exists something.
When asked to "Prove that there exists such x that y" , is giving such "x" enough as a solution or do you need to find like a general formula or something? For example, if asked to "prove that there exists n ≤ d such that d|2^(n)−1". One solution…
kiasy
- 127
2
votes
1 answer
Are any proofs of undecidability in ZFC also proofs of truth for properties of numbers?
Look at statements such as these:
All nontrivial zeroes of the Riemann Zeta function lie on the critical line.
Every even integer greater than 2 can be expressed as the sum of two primes.
Every perfect number is even.
Suppose that any statement…
orlp
- 10,508
2
votes
0 answers
Provably total functions?
I want to know what does it mean when we say for example
$$f(x)=2^x$$ is provably total in Peano arithmetic? Also what's the diffrence between provably total and provably recursive?
Erfan Khaniki
- 717
1
vote
2 answers
Are there thoughtfully simple concepts that we cannot currently prove?
I was driving and just happened to wonder if there existed some concepts that are simple to grasp, yet are not provable via current mathematical techniques. Does anyone know of concepts that fit this criteria?
I imagine the level of simple could…
agweber
- 125
1
vote
2 answers
Is there such a function $f(a,b)=k$ where each value of $k$ appears only once for all integer values of $a$ and $b$?
Suppose we have $f(a,b)=k$ such that $k$ is an integer when $a$ and $b$ are integers. Is there such a function where each value of $k$ appears only once for all integer values of $a$ and $b$?
e.g the function $f(a,b)=4ab+3a+2b$ satisfies the…
user406613
1
vote
0 answers
When k drawings are made in succession from n balls and every time ball is white then chance that next ball will be white
A bag contains n balls; k drawings are made in succession, and the ball on each occasion is found to be white. Find the chance that the next drawing will give a white ball (i) if balls are replaced (ii) if balls aren't replaced
I found the question…
nikola
- 119
1
vote
2 answers
Do mathematicians ever prove that something can or can't be proved?
I was just idly thinking about things people have a hard time proving, like P=NP, etc, and wondering if instead it could be proved that it's provable or unprovable.
Is that a thing? Does that ever happen?
1
vote
1 answer
provability of a mathematical statement
Is it possible to prove that a non-axiom statement is not mathematically provable with current accepted axioms of mathematics?
Note that this is not a question of proving if it is a true or false statement, but a proof that it is impossible to make…
Rory Grice
- 462
0
votes
2 answers
It is possible to calculate this probability
Suppose two Soccer Teams A and B.
Each of them is assigned a "potential Winner"% (PA and PB) as a result of the computation of a series of data: total victories, confrontations ... that they have obtained so far.
If the two Teams meet in a match It…
neg1414
- 3
0
votes
1 answer
Prove if $m \in \mathbb{Z}$ and $n \in \mathbb{Z} \backslash \{ −1, 0 \}$, $\frac{m + 1}{n+1}$>$\frac{m}{n}$
How to prove if $m \in \mathbb{Z}$ and $n \in \mathbb{Z} \backslash \{ −1, 0 \}$ then $\frac{m + 1}{n+1} > \frac{m}{n}$ ?
I started by realizing $n \subset m$ and if we choose $x \in n$ it also means that $x \in m$. I don't know if I need to do that…
Joe
- 599
0
votes
0 answers
Are there any conjectures known not to be independent that have neither been proven true or false?
Are there any known conjectures that have been shown not to be independent of whatever system they target (i.e. provable), but have not yet been shown to be true or false?
AlphaModder
- 569
-2
votes
1 answer
Proving $\frac{0}{0} = \infty$
I once heard my mathematics teacher say that $\frac{0}{0} = \infty$ and she said proving this is difficult.
How would I prove this?
Then will $1 \times 0 = \infty$ as well or just $0$?
