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a) Is there an x such that [x] = -1? Explain your reasoning.
b) If [x] = 3 what are the possible values for x?
c) What is your best definition of absolute value?
I'll try this as an analogy. When manipulating absolute values I try to imagine then this way--|x| is the real positive square root of x^2.
a) if x=-1 then x^2=1, and x is the positive square root of 1, or x=1. So x=1 and x=-1 is a
contradiction. So x cannot be -1.
b) if |x|=3 then x^2=9, and the squareroot of 9 is +/-3. But x is the
positive square root of 9 which can only be +3.
c) see 1st pp after Quote.
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