- #1

Valhalla

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let [tex] B = \{x\in\mathbb{R} : sinx \geq 0 \} [/tex]

find the supremum and infimum of this set.

Ok well, since it is periodic I guess the point would be to note that the set will repeat ever [tex]2\pi[/tex]

So then if we consider just between 0 and [tex]2\pi[/tex]

supremum = [tex]\pi[/tex]

infimum = 0

if we consider all [tex]\mathbb{R}[/tex]

here is where I'm confused. The supremum would just be the [tex]N\pi[/tex] when N is an odd integer. Should I just state the function is periodic it will repeat between 0 and [tex]2\pi[/tex]

find the supremum and infimum of this set.

Ok well, since it is periodic I guess the point would be to note that the set will repeat ever [tex]2\pi[/tex]

So then if we consider just between 0 and [tex]2\pi[/tex]

supremum = [tex]\pi[/tex]

infimum = 0

if we consider all [tex]\mathbb{R}[/tex]

here is where I'm confused. The supremum would just be the [tex]N\pi[/tex] when N is an odd integer. Should I just state the function is periodic it will repeat between 0 and [tex]2\pi[/tex]

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