By Abhijit Dasgupta

ISBN-10: 1461488540

ISBN-13: 9781461488545

What's a bunch? what's infinity? what's continuity? what's order? solutions to those basic questions bought via overdue nineteenth-century mathematicians similar to Dedekind and Cantor gave beginning to set thought. This textbook provides classical set conception in an intuitive yet concrete manner.

To let flexibility of subject choice in classes, the publication is equipped into 4 rather self sufficient elements with exact mathematical flavors. half I starts off with the Dedekind–Peano axioms and ends with the development of the genuine numbers. The center Cantor–Dedekind thought of cardinals, orders, and ordinals seems partially II. half III makes a speciality of the true continuum. ultimately, foundational matters and formal axioms are brought partly IV. every one half ends with a postscript bankruptcy discussing themes past the scope of the most textual content, starting from philosophical comments to glimpses into landmark result of sleek set concept resembling the solution of Lusin's difficulties on projective units utilizing determinacy of countless video games and big cardinals.

Separating the metamathematical matters into an not obligatory fourth half on the finish makes this textbook appropriate for college kids attracted to any box of arithmetic, not only for these making plans to specialise in good judgment or foundations. there's sufficient fabric within the textual content for a year-long direction on the upper-undergraduate point. For shorter one-semester or one-quarter classes, quite a few preparations of issues are attainable. The booklet can be an invaluable source for either specialists operating in a appropriate or adjoining quarter and newcomers eager to examine set thought through self-study.