Let a be an arbitrary real number. Show that there exists uniquely k Z such...

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Let a be an arbitrary real number. Show that there exists uniquely k € Z such that k < x <k+1. (The number k as in the statement is called the floor of r and is denoted by [2].) Let a be an arbitrary real number. Show that there exists uniquely k € Z such that k < x <k+1. (The number k as in the statement is called the floor of r and is denoted by [2].)

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