1. Let ? < ? be real numbers and N ? N.
(a). Show that if ? ? ? > N then there are at least Ndistinct integers strictly between ? and ?.
(b). Show that if ? > ? are real numbers then there is arational number q ? Q such ? > q > ?.
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2. Let x, y, z be real numbers.The absolute value of x isdefined by
|x|= x, if x ? 0 ,
?x, if x < 0
Define the following statements. Assume that the product of twopositive real numbers is positive.
(a). Show that |x?y| = |y?x|.
(b). Show that if z<0 and x ? y, then zy ? zx.
(c). Show that |x+y| ? |x|+|y|.
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Answer both questions plz. Will rate.
