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  3. 1. let ? < ? be real numbers and n ? n. (a). sh

1. Let ? < ? be real numbers and N ? N. (a). Show that if...

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Advance Math

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|.

***********************************************************************************************

Answer both questions plz. Will rate.

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