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Re: Integer question
Posted:
Aug 6, 2012 12:44 PM
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> Hi,
>
> I'm having trouble understanding "the least integer
> greater than or equal to z" in the following
> question:
>
> 96. For all Z, [z] denotes the least integer greater
> than or equal to z. Is [x] = 0?
>
> s1) -1 < x < -0.1
> s2) [x + 0.5] = 1
>
> What does "the least integer greater than or equal to
> z" mean? Can someone explain it to me in English?
>
>
Consider two cases:
1. z is an integer. Let z=n
Then n, n+1, n+2, .... are all integers >= n
And the least of these is n
So "the least integer >= z" is n.
That is [z]=n
2. z is not an integer. Let z=n+d where 0<d<1
Then n+1, n+2, n+2, .... are all integers >= n
And the least of these is n+1
So "the least integer >= z" is n+1.
That is [z]=n+1
Q 96. asks if [x]=0 in two cases:
s1) -1<x<-0.1
In this case x=-1+d where 0<d<0.9
So [x] = -1+1 =0 and the answer is Yes.
s2) [x+0.5] = 1
So 0<(x+0.5)<=1
So -0.5<x<=0.5
So the answer is not Yes for the whole range,
so it must be No.
More specifically:
For -0.5<x<=0 the answer is Yes,
but for 0<x<=0.5 the answer is No.
Regards, Peter Scales.
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