(1) For each of the following definitions, (a) rewrite the definition using math symbols wherever possible.; (b) write the negation of the definition using math symbols wherever possible; (c) write...

Extracted text: (1) For each of the following definitions, (a) rewrite the definition using math symbols wherever possible.; (b) write the negation of the definition using math symbols wherever possible; (c) write the negation of the definition in English. (1.1) A function f: R → R is unbounded if and only if given any M E R, there exists an x E R such that the absolute value of f (x) is greater than or equal to M. (1.2) A subset K of R is compact if and only if for any collection of open subsets of {U;}, whose union contains the set K, there exists a finite sub-collection {Uj, Uja,' Uin} of {U;}1 such ... that K is contained in the union of this finite sub-collection of sets.