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ADVANCED MATH Prove that (a) for every natural number n, $\dfrac{1}{n}\leq 1$. (b) there is a natural number M such that for all natural numbers n $>$ M, $\dfrac{1}{n}<0.13$. (c) for every natural number n, there is a natural number M such that 2n $<$ M. (d) for every natural number n, $\dfrac{1}{n}\< M$. (e) there is no largest natural number. (f) there is no smallest positive real number. (g) For every integer k there exists an integer m such that for all natural numbers n, we have $0\leq m+5<n$. (h) For every natural number n there is a real number r such that for all natural numbers m and t, if $t>m>\dfrac{1}{r}$ then $t+n>102$. (i) there is a natural number K such that $\dfrac{1}{r^2} < 0.01$ whenever r is a real number larger than K. (j) there exist integers L and G such that L $<$G and for every real numberx, if $L < x < G$, then $40 > 10 - 2x > 12$. (k) there exists an odd integer M such that for all real numbers r larger than 1 M, we have $\dfrac{1}{2r}< 0.01$. (l) for every natural number x, there is an integer k such that 3.3x + k $<$50. (m) there exist integers $x < 100$ and $y < 30$ such that $x + y < 128$ and for all real numbers rands, if $r > x$ and $s > y$, then $(r - 50)(s - 20) > 390$. (n) for every pair of positive real numbers x and y where $x < y$, there exists a natural number M such that if n is a natural number and $n > M$, then $\dfrac{1}{n}<$ (y - x). Verified answer
ADVANCED MATH Verified answer
ADVANCED MATH Verified answer
ADVANCED MATH Verified answer Other Quizlet setsRelated questionsWhat is the process of selecting an alternative course of action that will solve a problem?Decision making is the process of selecting an alternative course of action that will solve a problem.
Which type of decisionThere are three decision-making conditions. As a general rule, one should use the bounded rationality model with group decision making when a nonprogrammed decision with high risk or uncertainty exists.
What standard is used to judge a possible solution?A criterion is a standard, rule, or test by which something can be judged—a measure of value. Problem solvers develop criteria to assist them in formulating and evaluating possible solutions to a problem. Criteria are based on facts or assumptions.
Is the attractiveness and closeness group members have for one another and for the group?The attractiveness and closeness group members have for one another and for the group. Factors influencing cohesiveness are objectives, size, homogeneity, participation, competition, and success.
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Synectics is the process of suggesting many alternatives, without evaluation, to solve a problem.
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