MTH241
Question: Every nonempty subset of N has a least element. This is called a property of N.
Answer: well – ordering
Question: If \\(f : X Wrightarrow Y\\) is a function and if \\( X_1 Wsubset XW), we can define a function \\(f_1 : X_1 Wrightarrow YW) by W(f_1 (x) : = f(x)W) for \\(x Win XW). The function W(f_1 W) is called the of ftoW(X_1W).
Answer: restriction
Question: Subsequences of convergent sequences to another limit.
Answer: converge
Question: Let S be a subset of N such that \\ (1 Win SW) and for every W(k Win NW), if W(W{1, 2, Wldots kW} Wsubseteq SW), then W(k + 1 Win SW). Then S = N. This is called principle of induction.
Answer: strong
Question: For each \\(n Win NW), the sum of the first n natural numbers is given by the formula
Answer: W(Wfrac{1}{2} n(n + 1)W)
Question: What is the composite function W ((g Wcirc f)(x)\\), if \\(f(x) = 2 – xA3\\) and \\ (g(x) = xA3\\)?
Answer: \\(\\sq rt[3]{2-xA3}\\)
Question: Cauchy sequence of real numbers is
Answer: bounded
Question: Let R be a set of real numbers, If \\(a Win RW) and W(a Wneq OW), then W(aA2W)
Answer: > 0
Question: There is a nonempty subset P of R, called the set of positive real numbers, If a, b belong to P, then a + b belongs to
Answer: P
Question: Let A: = \\(\\{x: x\\in N, x Wleq 15\\}\\), B: = \\(\\{5x – 2, x \\in N\\}\\) and C:= \\(\\{4x + 1, x\\in NW). Determine \\(A Wcap B Wcap CW).
Answer: W(W{13W}W)
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