Mathematics, 30.03.2020 23:12, kaiyerecampbell95
A subset $S \subseteq \mathbb{R}$ is called open if for every $x \in S$, there exists a real number $\epsilon > 0$ such that $(x-\epsilon, x \epsilon) \subseteq S$. A subset $T \subseteq \mathbb{R}$ is called closed if $\mathbb{R} \setminus T$ is open. (a) Show that an open interval is open and that a closed interval is closed. (b) Show that $\emptyset$ and $\mathbb{R}$ are the only subsets of $\mathbb{R}$ that are both open and closed. (This is very hard. At least try to convince yourself that $\emptyset$ and $\mathbb{R}$ are both open and closed. Showing there is no other set that is both open and closed is quite difficult.) (c) Show that an arbitrary union of open intervals is open. (d) Show that an arbitrary union of closed intervals need not be closed. (Hint: in light of the definition of closed, this is the same thing as showing that an arbitrary intersection of open intervals need not be open.)
Answers: 3
Mathematics, 21.06.2019 12:30, geometryishard13
—the graph shows how fast a strand of human hair grows. how many inches would the hair have grown in 5 months
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Mathematics, 21.06.2019 17:30, rwbrayan8727
Marco has $38.43 dollars in his checking account. his checking account is linked to his amazon music account so he can buy music. the songs he purchases cost $1.29. part 1: write an expression to describe the amount of money in his checking account in relationship to the number of songs he purchases. part 2: describe what the variable represents in this situation.
Answers: 2
A subset $S \subseteq \mathbb{R}$ is called open if for every $x \in S$, there exists a real number...
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