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Jordan G
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5 votes
2 answers
101 views

How to prove that $\sup(A-B) = \sup(A) - \inf(B)$?

3 votes
3 answers
64 views

Let $x \in (0,1).$ How to show that $x \in \bigcup \left(0, \frac{n}{n+1}\right)$?

1 vote
1 answer
21 views

Let $\mathcal{A}= \{A_n = \left(0, \frac{n}{n+1} \right) \ | \ n \in \mathbb{N} \}$. Prove that $\bigcup \mathcal{A}\subseteq (0,1)$.

1 vote
1 answer
71 views

How to express a function into powers of $(x-1)$ and $(y-2)$ using Taylor's formula?

1 vote
1 answer
62 views

If $a\leq x_n \leq b$, then $a \leq \lim x_n \leq b$ [duplicate]

1 vote
1 answer
48 views

Let $\Gamma \neq \emptyset$. Also $\Gamma \subseteq \Omega$. Show that $\bigcap \Omega \subseteq \bigcap \Gamma.$

0 votes
0 answers
60 views

Prove that if A is bounded in $ \mathbb{R}$, then $\inf(A) \leq \sup(A)$

0 votes
0 answers
50 views

What is the power series solution of $3y'' + xy' + y= 0$, when $x=0$ is an ordinary point?

0 votes
1 answer
27 views

Simplifying equations of partial derivatives by substitution

0 votes
0 answers
12 views

Let $A \subset \mathbb{R}$ and $c \in \mathbb{R}$. If $c \geq 0$, then $\sup{cA} = c\sup{A}$ [duplicate]

0 votes
1 answer
53 views

How to show that the set $A=[a,b)$ is not open nor closed? [duplicate]

0 votes
1 answer
128 views

Prove that the closed interval [a, b] is compact.