Laurel S.

asked • 09/05/14

what is the value of [x]+[-x] where x is a real number?

is this as simple as just plugging in real numbers for x? if so, let's say x=1 then we have [1]+[-1] would be 0 so the value for all real numbers in this particular summation would always be zero...?
 
is that right?

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Phillip R. answered • 09/05/14

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if this is the greatest integer function, then [x] = x and [-x] = -x - 1
 
Therefore the sum is x - x - 1 = -1
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Aaron M.

The greatest integer function is defined by "the greatest integer less than or equal to x." Thus if x is an integer then [x] = x and [-x] = -x. If x is not an integer [x] = x(truncated at the decimal) and [-x] = (-x - 1) (truncated at the decimal.
 
ex. x = 5
[x] + [-x] = 5 - 5 = 0
 
ex. x = 3.14
[x] + [-x] = 3 + (-4) = -1
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09/26/15

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