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Nov
18
comment Help needed with an equivalence relation task on natural numbers
Your translation isn’t quite right. It should be: Prove that all natural numbers $x$ and $y$ that are elements of $E$ are such that $x\sim y$. I’ll fix it in the question.
Nov
18
comment Mathematics sign for ceil and floor functions
As @Christopher says, it’s the ceiling function, written $\lceil x\rceil$.
Nov
18
comment How to prove or disprove finiteness?
@user64494: Neither am I; I’m not even an algebraist. I don’t want to say too much more, because it’s already a fairly substantial hint. (1) If $x\in G$ has finite order, how big is the subgroup $\langle x\rangle$ of $G$? (2) Up to isomorphism there is only one infinite cyclic group, $\Bbb Z$; what subgroups does it have?
Nov
18
answered How to prove or disprove finiteness?
Nov
18
comment Let $A=\{2a:a\in\omega\}$ be the set of even natural numbers
@derivative: According to what you wrote in the question, you are to find a representation of the equivalence classes; that’s not the same thing as finding one representative of each class. It requires you to find a nice description of the classes.
Nov
18
answered Drawing a hasse diagram of a poset.
Nov
18
answered Is every function from $\aleph_0 \to \aleph_2$ bounded?
Nov
18
answered Let $A=\{2a:a\in\omega\}$ be the set of even natural numbers
Nov
18
answered Alternative ways to write $ k \binom{n}{k} $
Nov
18
comment Pumping Lemma - Clarification of Usage
@EggHead: Ah, okay. Yes, as long as $|w|\ge p$, $w$ can be as long as you need to make the proof work.
Nov
18
comment Calculus integration problem. [HW help]
@Prahlad: I’d interpret as $\int x^2\,dx$, but I’d also explain that I was doing so, interpreting juxtaposition as product the product orange segment with orange segment rather than as two orange segments.
Nov
18
comment Solving a bijective function task
@Dabbish: You’re welcome!
Nov
18
revised Find upper and lower bounds to the function $f(n)=1\cdot3\cdot5\cdot\ldots\cdot(2n-1)$ where $n\in\Bbb N$
LaTeX.
Nov
18
comment Solving a bijective function task
@Henning: It was originally equality and bijections, and I apparently overlooked the second when I changed the first. Thanks.
Nov
18
revised Solving a bijective function task
edited body
Nov
18
comment Optimal vs Optimum
Optimum as an adjective goes back at least to $1885$, which is less than $40$ years after the earliest OED citation for it as a noun.
Nov
18
revised Set-theory, functions between sets
edited body
Nov
18
comment Set-theory, functions between sets
@derivative: An arbitrary proper subset of $\omega$. Sorry: I forgot that $A$ was already in use; I’ve changed it to $S$.
Nov
18
answered Solving a bijective function task
Nov
18
answered Set-theory, functions between sets