#Hi! What does the square brackets mean?

17 messages · Page 1 of 1 (latest)

glad totem
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I assume it's not abs, like for 5, I believe I first calculate the lim of g(x) and then use the outside brackets? But what exactly do I apply for the outside brackets? And for 6, how do I proceed because the square brackets are inside the round ones? Thanks!!

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frank prairieBOT
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tawny gorge
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So, for example, ⌊2.1⌋ = 2, ⌊1.9⌋ = 1, ⌊-1.9⌋ = -2. And for any integer n we obviously have ⌊n⌋ = n.

glad totem
tawny gorge
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You're correct about (5). As for (6), note that ⌊x⌋ behaves in a simple way for x -> 0-.

glad totem
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so i js take the lim and round down?

tawny gorge
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Although...

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No, I don't think it's that simple.
For (5) you need to consider how exactly g(x) approaches its limit.

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So, for example, for x -> 0- we have ⌊x^2⌋ -> 0, but ⌊x^3⌋ -> -1, since one x^2 goes to 0 from above, but x^3 goes from below.

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I don't think there's a particularly simple expression in (5) for a general g(x).
(6) can be written generally, though.

glad totem
tawny gorge
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You're welcome!

glad totem
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+close

simple heraldBOT
# glad totem +close
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simple heraldBOT
# simple herald

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