2. Chapter 13, Problem 4: Prove the following using the definition of infinite: (a) The interval (0, 1) is infinite. (b) The interval (a, b) \subset \mathbb{R} is infinite.
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1.a. Define what is an injective function, and what is an onto (surjective) function. b. Give an example when f is injective but not onto. c. Give an example when f is onto but not injective. 2. Complete the definition: Let A be a non empty set. A is called countable if... 3. Let A ⊆ ℕ. Prove that if A is neither empty nor finite, then it is countably infinite. 4. Prove that there is a bijection between the intervals (1,3) and (-2,4).
Adi S.
Let a function $f:(0, \infty) \rightarrow(0, \infty)$ be defined by $f(x)=\left|1-\frac{1}{x}\right|$. Then $f$ is: (a) not injective but it is surjective (b) injective only (c) neither injective nor surjective (d) both injective as well as surjective
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