Inequalities and Absolute Value
... Let’s now consider two relations on the set of real numbers. These are the relations of order or inequality known as less than or greater than. The set of real numbers is an ordered set. Given any two numbers, we can determine whether one number is less than, equal to, or greater than the other. Let ...
... Let’s now consider two relations on the set of real numbers. These are the relations of order or inequality known as less than or greater than. The set of real numbers is an ordered set. Given any two numbers, we can determine whether one number is less than, equal to, or greater than the other. Let ...
6.4 Recursion Formulas
... calculate any term in a sequence without knowing the previous term. For example, the tenth term in the sequence determined by the formula tn = 2n + 3 is 2(10) + 3, or 23. It is sometimes more convenient to calculate a term in a sequence from one or more previous terms in the sequence. Formulas that ...
... calculate any term in a sequence without knowing the previous term. For example, the tenth term in the sequence determined by the formula tn = 2n + 3 is 2(10) + 3, or 23. It is sometimes more convenient to calculate a term in a sequence from one or more previous terms in the sequence. Formulas that ...
Automata and Rational Numbers - the David R. Cheriton School of
... Case 2: If α ∈ S and α is “big”, say α > k n , then the numerator can be pumped, but the denominator stays the same. So the denominator must divide [uvw ]k − [uw ]k . But this is k |w | ([uv ]k − [u]k ), and |uv | ≤ n, so each denominator must divide a bounded number, times a power of k. So the set ...
... Case 2: If α ∈ S and α is “big”, say α > k n , then the numerator can be pumped, but the denominator stays the same. So the denominator must divide [uvw ]k − [uw ]k . But this is k |w | ([uv ]k − [u]k ), and |uv | ≤ n, so each denominator must divide a bounded number, times a power of k. So the set ...
