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Having an estimate $hat{p}$ of $p$, what can we say about $1-hat{p}$?

First, let us define:$epsilon$-additive approximation:$$hat{p} in big[ p -epsilon, p + epsilon big]$$$epsilon$-multiplicative approximation:$$hat{p} in big[ p cdot (1-epsilon), ...

Mathematics Asked on 2 years ago

Set of subspaces of vector space

Let $V$ be a (real) vector space. Consider the set $mathscr{V}$ consisting of all subspaces of $V .$ Equipping $mathscr{V}$ with the addition of subspaces, is...

Mathematics Asked by maths student on 2 years ago

If $x$ is a fixed point of a continuous function $f$, there is an open neighborhood $N$ of $x$ with $f(N)subseteq N$

Let $Omega$ be an open subset of a topological space $E$ and $xinOmega$ be a fixed point of a continuous function $f:Omegato E$.How can we show...

Mathematics Asked on 2 years ago

On closed balls of a subset of a metric space

Let $X$ be a vector space and let $A$ be a subset of $X$. Let $d$ be a metric on $X$ which is not induced...

Mathematics Asked by serenus on 2 years ago

What is known about primorial and factorial minus one prime?

$324$ is an example of an integer such that both $324!-1$ and $primorial(324)-1$ are primes.Are there other examples?Is there some condition to be $n!...

Mathematics Asked by Enzo Creti on 2 years ago

Ring and elements with multiplicative decompositions with same sum

Is there any commutative unitary ring $(R,+,cdot,0,1)$, that is not an integral domain, with an element $xneq 1,0$ that presents at least two distinct multiplicative "proper" decompositions (i.e....

Mathematics Asked on 2 years ago

Existance and example of extraordinary set and set of all such extraordinary sets in the context of Russels paradox

I recently started studying elementary set theory on my own. I understood Russels paradox. By assuming set of all ordinary sets it leads to contradiction. Now if i think about...

Mathematics Asked by Nascimento de Cos on 2 years ago

Inverse of stereographic projection

I am trying to compute the inverse of $$f(theta,phi) = left(frac{costheta sinphi}{1-cosphi}, frac{sintheta sinphi}{1-cosphi}right)$$ but I lack some basic knowledge on how I can do that. Could please provide...

Mathematics Asked by Thoth on 2 years ago

Euclidean mapping question

Give $A$ is Euclidean domain and $delta: Asetminus left{0right} to mathbb{N}$ is Euclidean mapping. I have prove that "$A$ is a field if and only if ...

Mathematics Asked by Tung Nguyen on 2 years ago

Optimal guessing strategy in hangman word game?

Suppose we are playing the game hangman. My opponent picks a word at random from the dictionary, which we both have access to during the game. Once...

Mathematics Asked by zfj3ub94rf576hc4eegm on 2 years ago

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